Elliptic Interface Problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes
Numerical Analysis
2026-03-03 v2 Numerical Analysis
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.
Cite
@article{arxiv.2507.06740,
title = {Elliptic Interface Problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes},
author = {Daniela Capatina and Aimene Gouasmi},
journal= {arXiv preprint arXiv:2507.06740},
year = {2026}
}