A Posteriori Error Estimators for Elliptic Equations with Discontinuous Diffusion Coefficients

We regard linear elliptic equations with discontinuous diffusion coefficients in two and three space dimension with varying boundary conditions. The problem is discretized with linear Finite Elements. We propose the treatment of the arising singularities within an adaptive procedure based on a posteriori error estimators. Within this concept no a priori data like the degree of the singularity is needed. We introduce the class of quasi-monotone distributed diffusion coefficients. Within this class an interpolation operator as well as a posteriori error estimators with bounds which are independend of the variation of the diffusion coefficients are derived. In numerical examples we confirm robustness of the error estimators and show that on adaptively refined meshes the reduction of the error is optimal with respect to the number of unknows. TABLE OF CONTENTS