2000 character limit reached
A fixed-stress type splitting method for nonlinear poroelasticity
Published 29 Dec 2023 in math.NA and cs.NA | (2312.17698v1)
Abstract: In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are typically used to study biological structures like tissues, organs, cartilage and bones, which are known for a nonlinear dependence of their permeability/hydraulic conductivity on solid dilation. We formulate (extend to the present situation) one of the most popular splitting schemes, namely the fixed-stress split method for the iterative solution of the coupled problem. The method is proven to converge linearly for sufficiently small time steps under standard assumptions. The error contraction factor then is strictly less than one, independent of the Lam\'{e} parameters, Biot and storage coefficients if the hydraulic conductivity is a strictly positive, bounded and Lipschitz-continuous function.
- Detournay, E., Cheng, A.-D.: Poroelastic response of a borehole in non-hydrostatic stress field. Int. J. Rock Mech. Mining Sci. 25(25), 171–182 (1988) Jha and Juanes [2014] Jha, B., Juanes, R.: Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering. Water Resources Research 50(5), 3776–3808 (2014) Cowin [1999] Cowin, S.C.: Bone poroelasticity. Journal of biomechanics 32(3), 217–238 (1999) Roose et al. [2003] Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Jha, B., Juanes, R.: Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering. Water Resources Research 50(5), 3776–3808 (2014) Cowin [1999] Cowin, S.C.: Bone poroelasticity. Journal of biomechanics 32(3), 217–238 (1999) Roose et al. [2003] Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cowin, S.C.: Bone poroelasticity. Journal of biomechanics 32(3), 217–238 (1999) Roose et al. [2003] Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. 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[2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cowin, S.C.: Bone poroelasticity. Journal of biomechanics 32(3), 217–238 (1999) Roose et al. [2003] Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Roose, T., Netti, P.A., Munn, L.L., Boucher, Y., Jain, R.K.: Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvascular research 66(3), 204–212 (2003) Carter and Wong [2003] Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. 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Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Carter, D.R., Wong, M.: Modelling cartilage mechanobiology. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358(1437), 1461–1471 (2003) Konofagou et al. [2001] Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Konofagou, E.E., Harrigan, T.P., Ophir, J., Krouskop, T.A.: Poroelastography: imaging the poroelastic properties of tissues. Ultrasound in medicine & biology 27(10), 1387–1397 (2001) Kyriacou et al. [2002] Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Kyriacou, S.K., Mohamed, A., Miller, K., Neff, S.: Brain mechanics for neurosurgery: modeling issues. Biomechanics and modeling in mechanobiology 1(2), 151–164 (2002) Bohr et al. [2022] Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bohr, T., Hjorth, P.G., Holst, S.C., Hrabětová, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.-A., Martens, E.A., Mori, Y., et al.: The glymphatic system: Current understanding and modeling. Iscience 25(9) (2022) Terzaghi et al. [1996] Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Terzaghi, K., Peck, R.B., Mesri, G.: Soil mechanics in engineering practice (1996) Biot [1941] Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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[2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: General theory of three-dimensional consolidation. Journal of applied physics 12(2), 155–164 (1941) Biot [195] Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics 26, 182–185 (195) Coussy [1995] Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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[2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Coussy, O.: Mechanics of porous continua. Wiley, West Sussex (1995) Showalter [2000] Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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[2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. 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Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E.: Diffusion in poro-elastic media. J. Math. Anal. Appl. 251(1), 310–340 (2000) Showalter and Stefanelli [2004] Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Showalter, R.E., Stefanelli, U.: Diffusion in poro-plastic media. Math. Methods Appl. Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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Sci. 27(18), 2131–2151 (2004) Mikelić and Wheeler [2012] Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system. J. Math. Phys. 53(12), 123702–15 (2012) Hiltunen [1995] Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hiltunen, K.: Mathematical and numerical modelling of consolidation processes in paper machines. Jyväskylän Yliopisto (1995) Raghavan and Chin [2002] Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Raghavan, R., Chin, L.Y.: Productivity changes in reservoirs with stress-dependent permeability. In: SPE Annual Technical Conference and Exhibition, p. 77535 (2002) Chin et al. [2000] Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. 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[2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Chin, L., Raghavan, R., Thomas, L.: Fully coupled geomechanics and fluid-flow analysis of wells with stress-dependent permeability. Spe Journal 5(01), 32–45 (2000) Barbeiro and Wheeler [2010] Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Barbeiro, S., Wheeler, M.F.: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability. Computational Geosciences 14, 755–768 (2010) Cao et al. [2013] Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. 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[2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. 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[2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Cao, Y., Chen, S., Meir, A.: Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems-Series B 18(5) (2013) Cao et al. [2014] Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Cao, Y., Chen, S., Meir, A.: Steady flow in a deformable porous medium. Mathematical Methods in the Applied Sciences 37(7), 1029–1041 (2014) Cao et al. [2015] Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Cao, Y., Chen, S., Meir, A.: Quasilinear poroelasticity: Analysis and hybrid finite element approximation. Numerical Methods for Partial Differential Equations 31(4), 1174–1189 (2015) Bociu et al. [2016] Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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[2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Bociu, L., Guidoboni, G., Sacco, R., Webster, J.T.: Analysis of nonlinear poro-elastic and poro-visco-elastic models. Archive for Rational Mechanics and Analysis 222, 1445–1519 (2016) van Duijn and Mikelić [2023] Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Duijn, C., Mikelić, A.: Mathematical theory of nonlinear single-phase poroelasticity. Journal of Nonlinear Science 33(3), 44 (2023) Borregales et al. [2018] Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Radu, F.A., Kumar, K., Nordbotten, J.M.: Robust iterative schemes for non-linear poromechanics. Computational Geosciences 22, 1021–1038 (2018) Borregales et al. [2019] Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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[2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. 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[2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. 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Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Borregales, M., Kumar, K., Radu, F.A., Rodrigo, C., Gaspar, F.J.: A partially parallel-in-time fixed-stress splitting method for biot’s consolidation model. Computers & Mathematics with Applications 77(6), 1466–1478 (2019) Borregales Reverón et al. [2021] Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Borregales Reverón, M.A., Kumar, K., Nordbotten, J.M., Radu, F.A.: Iterative solvers for biot model under small and large deformations. Computational Geosciences 25, 687–699 (2021) Kumar et al. [2016] Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. 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International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Kumar, K., Almani, T., Singh, G., Wheeler, M.F.: Multirate undrained splitting for coupled flow and geomechanics in porous media. In: Numerical Mathematics and Advanced Applications—ENUMATH 2015. Lect. Notes Comput. Sci. Eng., vol. 112, pp. 431–440. Springer, ??? (2016) Almani et al. [2016] Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Engrg. 311, 180–207 (2016) Allen [2009] Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Allen, D.R.: Stability, accuracy, and efficiency of sequential methods for coupled flow and geomechanics. Technical Report SPE119084, The SPE Reservoir Simulation Symposium, Houston, Texas (2009) White et al. [2016] White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. 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Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Engrg. 303, 55–74 (2016) Castelletto et al. [2016] Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Castelletto, N., White, J.A., Ferronato, M.: Scalable algorithms for three-field mixed finite element coupled poromechanics. J. Comput. Phys. 327, 894–918 (2016) Gaspar and Rodrigo [2017] Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Gaspar, F.J., Rodrigo, C.: On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics. Comput. Methods Appl. Mech. Engrg. 326, 526–540 (2017) Hong et al. [2019] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. 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[2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. 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[2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. 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Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Conservative discretizations and parameter-robust preconditioners for biot and multiple-network flux-based poroelasticity models. Numerical Linear Algebra with Applications 26(4), 2242 (2019) Lee et al. [2017] Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. 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[2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. 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[2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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[2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Lee, J.J., Mardal, K.-A., Winther, R.: Parameter-robust discretization and preconditioning of Biot’s consolidation model. SIAM J. Sci. Comput. 39(1), 1–24 (2017) Hong and Kraus [2018] Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Hong, Q., Kraus, J.: Parameter-robust stability of classical three-field formulation of biot’s consolidation model. ETNA - Electronic Transactions on Numerical Analysis 48, 202–226 (2018) Hong et al. [2020a] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale modeling & simulation 18(2), 916–941 (2020) Hong et al. [2020b] Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Hong, Q., Kraus, J., Lymbery, M., Philo, F.: Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models. Math. Models Methods Appl. Sci. 30(13), 2523–2555 (2020) Settari and Mourits [1998] Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Settari, A., Mourits, F.M.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219–226 (1998) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. 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[2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: The gradient flow structures of thermo-poro-visco-elastic processes in porous media. arXiv preprint arXiv:1907.03134 (2019) Kim et al. [2011a] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Engrg. 200(13-16), 1591–1606 (2011) Kim et al. [2011b] Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Kim, J., Tchelepi, H.A., Juanes, R.: Stability and convergence of sequential methods for coupled flow and geomechanics: drained and undrained splits. Comput. Methods Appl. Mech. Engrg. 200(23-24), 2094–2116 (2011) Almani et al. [2020] Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Almani, T., Manea, A., Kumar, K., Dogru., A.H.: Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media. Computational Geosciences 24, 551–569 (2020) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Almani et al. [2017] Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Almani, T., Kumar, K., Wheeler, M.F.: Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics. Comput. Geosci. 21(5-6), 1157–1172 (2017) Mikelić and Wheeler [2013] Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455–461 (2013) Both et al. [2017] Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Both, J.W., Borregales, M., Nordbotten, J.M., Kumar, K., Radu, F.A.: Robust fixed stress splitting for Biot’s equations in heterogeneous media. Applied Mathematics Letters 68, 101–108 (2017) Storvik et al. [2019] Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Storvik, E., Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: On the optimization of the fixed-stress splitting for biot’s equations. International Journal for Numerical Methods in Engineering 120(2), 179–194 (2019) List and Radu [2016] List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- List, F., Radu, F.A.: A study on iterative methods for solving Richards’ equation. Computational Geosciences 20(2), 341–353 (2016) Both et al. [2019] Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Both, J.W., Kumar, K., Nordbotten, J.M., Radu, F.A.: Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media. Computers & Mathematics with Applications 77(6), 1479–1502 (2019) Hong et al. [2020] Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Hong, Q., Kraus, J., Lymbery, M., Wheeler, M.F.: Parameter-robust convergence analysis of fixed-stress split iterative method for multiple-permeability poroelasticity systems. Multiscale Model. Simul. 18(2), 916–941 (2020) Alnæs et al. [2015] Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Archive of Numerical Software 3(100) (2015) Logg et al. [2012] Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012) Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
- Logg, A., et al.: Automated solution of differential equations by the finite element method. Springer (2012)
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