Elliptic Interface Problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes

Abstract

This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging to the immersed Raviart-Thomas space. We establish sharp reliability and local efficiency of a new error estimator, which includes both volume and interface terms, carefully tracking the dependence of the efficiency constant on the diffusion coefficients and the mesh/interface configuration. Numerical results highlight the robustness of the proposed approach.