Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh (Communications in Computational Physics, 2018)
In this paper, we propose a new gradient recovery method for elliptic interfaceproblem using body-fitted meshes. Due to the lack of regularity of the solution atthe interface, standard gradient recovery methods fail to give superconvergent resultsand thus will lead to overrefinement when served as a posteriori error estimators. Thisdrawback is overcome by designing a new gradient recovery operator. We prove thesuperconvergence of the new method on both mildly unstructured meshes and adaptivemeshes. Several numerical examples are presented to verify the superconvergenceand its robustness as a posteriori error estimator.