Burman, Erik;
He, Cuiyu;
Larson, Mats G;
(2022)
A posteriori error estimates with boundary correction for a cut finite element method.
IMA Journal of Numerical Analysis
, 42
pp. 333-362.
10.1093/imanum/draa085.
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Abstract
In this work we introduce, analyze and implement a residual-based a posteriori error estimation for the CutFEM fictitious domain method applied to an elliptic model problem. We consider the problem with smooth (nonpolygonal) boundary and, therefore, the analysis takes into account both the geometry approximation error on the boundary and the numerical approximation error. Theoretically, we can prove that the error estimation is both reliable and efficient. Moreover, the error estimation is robust in the sense that both the reliability and efficiency constants are independent of the arbitrary boundary-mesh intersection.
| Type: | Article |
|---|---|
| Title: | A posteriori error estimates with boundary correction for a cut finite element method |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/draa085 |
| Publisher version: | https://doi.org/10.1093/imanum/draa085 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, fictitious domain, CutFEM, a posteriori error estimation, AMR, FICTITIOUS DOMAIN METHOD, ELLIPTIC PROBLEMS |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10143728 |
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