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In this paper, we propose a novel gradient recovery method for ellipticinterface problem using body-fitted mesh in two dimension. Due to the lack ofregularity of solution at interface, standard gradient recovery methods fail togive superconvergent results, and thus will lead to overrefinement when servedas a posteriori error estimator. This drawback is overcome by designing animmersed gradient recovery operator in our method. We prove thesuperconvergence of this method for both mildly unstructured mesh and adaptivemesh, and present several numerical examples to verify the superconvergence andits robustness as a posteriori error estimator.

Gradient recovery for elliptic interface problem: I. body-fitted mesh