| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1269 - 1295 | |
| DOI | https://doi.org/10.1051/m2an/2026036 | |
| Published online | 01 June 2026 | |
Elliptic interface problem approximated by CutFEM: I. flux recovery and numerical validation of adaptive mesh refinement
1
LMAP CNRS UMR 5142, University of Pau and Pays de l'Adour, 64013 Pau, France
2
The University of Georgia, Athens, GA 30602, USA
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
11
July
2025
Accepted:
13
April
2026
Abstract
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of an element-wise conservative flux from the CutFEM solution and its use in a posteriori error estimation. We introduce a hybrid mixed formulation with locally computable Lagrange multipliers and reconstruct a flux in the immersed Raviart-Thomas space. Based on this, we propose a new a posteriori error estimator that includes both volume and interface terms. We state here its robust reliability and local efficiency, which are proved in Part II of this work. The approach is validated through numerical experiments.
Mathematics Subject Classification: 65N15 / 65N30 / 65N50
Key words: Elliptic interface problem / CutFEM / conservative flux reconstruction / a posteriori error estimation / adaptive finite element methods / immersed Raviart-Thomas elements
© 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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.