Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh

Abstract

In this paper, we propose a new gradient recovery method for elliptic interface problem using body-fitted meshes. Due to the lack of regularity of the solution at the interface, standard gradient recovery methods fail to give superconvergent results and thus will lead to overrefinement when served as a posteriori error estimators. This drawback is overcome by designing a new gradient recovery operator. We prove the superconvergence of the new method on both mildly unstructured meshes and adaptive meshes. Several numerical examples are presented to verify the superconvergence and its robustness as a posteriori error estimator.