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

Daniela Capatina; Aimene Gouasmi

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arXiv · 2507.06740

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

Daniela Capatina·Aimene Gouasmi

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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.

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Daniela Capatina, Aimene Gouasmi. 2025-07-09. Elliptic Interface Problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes. https://arxiv.org/abs/2507.06740

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