On the Stabilized Mixed Discontinuous Formulation for Darcy Flow

Abstract

In this talk, we provide a priori and a posteriori error analysis of an stabilized mixed discontinuous formulation for Darcy flow. The stabilized scheme is obtained through the introduction of suitable Galerkin least squares terms arising from constitutive and equilibrium equations. We use the
well-known Lax-Milgram lemma to show the well posedness of the resulting discrete scheme and then, under suitable assumptions, we derive the corresponding a priori error estimates and its optimal rate of convergence. In addition, we present a reliable and efficient a posteriori error estimator. Finally, several numerical results illustrating the performance of the augmented scheme and associated adaptive algorithms are reported.