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