Burman, Erik;
Hansbo, Peter;
Larson, Mats G;
(2023)
Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions.
Mathematics of Computation (MCOM)
10.1090/mcom/3875.
(In press).
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Abstract
We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution u ∈ Hs with s ∈ (1, 3/2]. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.
| Type: | Article |
|---|---|
| Title: | Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/mcom/3875 |
| Publisher version: | https://doi.org/10.1090/mcom/3875 |
| 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.v |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS 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 |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10175831 |
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