On the Efficiency of Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

The successful implementation of adaptive finite element methods based on a posteriori error estimates depends on several ingredients: an a posteriori error indicator, a refinement/coarsening strategy, and the choice of various parameters. The objective of the paper is to examine the influence of these factors on the performance of adaptive finite element methods for a model problem: the linear elliptic equation with strongly discontinuous coefficients. We derive a new a posteriori error estimator which depends locally on the oscillations of the coefficients around singular points. Extensive numerical experiments are reported to support our theoretical results and to show the competitive behaviors of the proposed adaptive algorithm.