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An overlapping local projection stabilization for Galerkin approximations of Darcy and Stokes problems (2009.00571v1)
Published 1 Sep 2020 in math.NA and cs.NA
Abstract: A priori analysis for a generalized local projection stabilized conforming finite element approximation of Darcy flow and Stokes problems is presented in this paper. A first-order conforming P1 finite element space is used to approximate both the velocity and the pressure. It is shown that the stabilized discrete bilinear form satisfy the inf-sup condition with respect to a generalized local projection norm. Moreover, a priori error estimates are derived for both problems. Finally, the validation of the proposed stabilization scheme is demonstrated with appropriate numerical examples.