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Finite element discretization of the steady, generalized Navier-Stokes equations with inhomogeneous Dirichlet boundary conditions (2310.04084v1)
Published 6 Oct 2023 in math.NA and cs.NA
Abstract: We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint. We establish (weak) convergence of discrete solutions as well as a priori error estimates for the velocity vector field and the scalar kinematic pressure. Numerical experiments complement the theoretical findings.