| Issue |
ESAIM: M2AN
Volume 60, Number 4, July-August 2026
|
|
|---|---|---|
| Page(s) | 1635 - 1665 | |
| DOI | https://doi.org/10.1051/m2an/2026043 | |
| Published online | 20 July 2026 | |
Elliptic interface problem approximated by CutFEM: II. A posteriori error analysis based on equilibrated fluxes
LMAP CNRS UMR 5142, University of Pau and Pays de l’Adour, 64013 Pau, France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
July
2025
Revised:
24
April
2026
Accepted:
4
May
2026
Abstract
This paper investigates an elliptic interface problem with discontinuous diffusion coefficients discretized by finite elements on unfitted meshes, employing the cut finite element method (CutFEM). 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 approach.
Mathematics Subject Classification: 65N15 / 65N30 / 65N50
Key words: A posteriori error analysis / CutFEM / adaptive mesh refinement / unfitted meshes / immersed Raviart–Thomas space
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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