An a posteriori error analysis of an augmented discontinuous Galerkin formulation for Darcy flow

Abstract

In this paper we develop an a posteriori error analysis for an augmented discontinuous Garlerkin formulation applied to the Darcy flow. More precisely, we derive a reliable and efficient a posteriori error estimator, which consists of residual terms. Finally, we present several numerical experiments, showing the robustness of the method and the theoretical properties of the estimator, thus confirming the capability of the corresponding adaptive algorithms to localize the inner layers, the singularities and/or the large stress regions of the exact solution.