A posteriori error estimates for enriched mixed formulations

Abstract

The purpose of this paper is to derive efficient and robust a posteriori error estimations for the enriched mixed methods proposed in [2, 4]. The general methodology is based on potential and flux reconstruction [6]. In the context of mixed methods for Poisson's problems only potential reconstruction is required since an equilibrated flux is already given by the method. The proposed scheme for potential reconstruction follows three main steps: solution of the problem using an enriched space configuration for flux and potential variables (no post processing is required), smoothing of the potential variable and solution of local Dirichlet problems with hybridization. Results of some verification tests are presented illustrating the performance of the scheme.