Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements

Abstract

This paper analyzes an equilibrated residual a posteriori error estimator for the diffusion problem. The estimator, which is a modification of those in [D. Braess and J. Schöberl, Math. Comput., 77 (2008), pp. 651–672; R. Verfürth, SIAM J. Numer. Anal., 47 (2009), pp. 3180–3194], is based on the Prager–Synge identity and on a local recovery of an equilibrated flux. Numerical results for an interface test problem show that the modification is necessary for the robustness of the estimator. When the distribution of diffusion coefficients is local quasi-monotone, it is shown theoretically that the estimator is robust with respect to the size of jumps.