Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method

Abstract

In this paper we analyze an a posteriori error estimator based on the equilibrated residual method. We prove that this estimator is asymptotically exact in the energy norm for regular solutions and $$O(h^{1+\alpha})\ (\alpha > 0)$$ meshes. Numerical examples are included to illustrate the theoretical results.