Energy Norm shape A Posteriori Error Estimation for Mixed Discontinuous Galerkin Approximations of the Stokes Problem

Abstract

In this paper, we develop the a posteriori error estimation of mixed discontinuous Galerkin finite element approximations of the Stokes problem. In particular, we derive computable upper bounds on the error, measured in terms of a natural (mesh-dependent) energy norm. This is done by rewriting the underlying method in a non-consistent form using appropriate lifting operators, and by employing a decomposition result for the discontinuous spaces. A series of numerical experiments highlighting the performance of the proposed a posteriori error estimator on adaptively refined meshes are presented.