A Posteriori Error Estimators for Elliptic Equations with Discontinuous Coefficients

We consider linear elliptic equations with discontinuous coefficients in two and three space dimensions with varying boundary conditions. The problem is discretized with linear finite elements. An adaptive procedure based on a posteriori error estimators for the treatment of singularities is proposed. Within the class of quasi-monotonically distributed coefficients we derive a posteriori error estimators with bounds that are independent of the variation of the coefficients. In numerical test cases we confirm the robustness of the error estimators and observe that on adaptively refined meshes the reduction of the error is optimal with respect to the number of unknowns.