Volume 55, Number 6, November-December 2021
|Page(s)||2759 - 2784|
|Published online||25 November 2021|
Flux recovery for Cut Finite Element Method and its application in a posteriori error estimation
LMAP & CNRS UMR 5142, University of Pau, 64013 Pau, France
2 Department of Mathematics, University of Georgia, Athens, GA 3060, USA
3 W University Blvd, School of Mathematics and Statistical Science, University of Texas Rio Grand Valley, Brownsville, TX 78520, USA
* Corresponding author: email@example.com
Accepted: 25 October 2021
In this article, we aim to recover locally conservative and H(div) conforming fluxes for the linear Cut Finite Element Solution with Nitsche’s method for Poisson problems with Dirichlet boundary condition. The computation of the conservative flux in the Raviart–Thomas space is completely local and does not require to solve any mixed problem. The L2-norm of the difference between the numerical flux and the recovered flux can then be used as a posteriori error estimator in the adaptive mesh refinement procedure. Theoretically we also prove the global reliability and local efficiency. The theoretical results are verified in the numerical results. Moreover, in the numerical results we also observe optimal convergence rate for the flux error.
Mathematics Subject Classification: 68Q25 / 68R10 / 68U05
Key words: CutFEM / a posteriori error estimation / flux recovery / adaptive mesh refinement
© The authors. Published by EDP Sciences, SMAI 2021
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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