Burman, E;
Hansbo, P;
Larson, MG;
Zahedi, S;
(2019)
Stabilized CutFEM for the convection problem on surfaces.
Numerische Mathematik
, 141
(1)
pp. 103-139.
10.1007/s00211-018-0989-8.
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Abstract
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a background mesh consisting of tetrahedra in an arbitrary way and the finite element space consists of piecewise linear continuous functions defined on the background mesh. The variational form involves integrals on the surface and the gradient jump stabilization term is defined on the full faces of the tetrahedra. The stabilization term serves two purposes: first the method is stabilized and secondly the resulting linear system of equations is algebraically stable. We establish stability results that are analogous to the standard meshed flat case and prove h3 / 2order convergence in the natural norm associated with the method and that the full gradient enjoys h3 / 4order of convergence in L2. We also show that the condition number of the stiffness matrix is bounded by h- 2. Finally, our results are verified by numerical examples.
| Type: | Article |
|---|---|
| Title: | Stabilized CutFEM for the convection problem on surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00211-018-0989-8 |
| Publisher version: | https://doi.org/10.1007/s00211-018-0989-8 |
| Language: | English |
| Additional information: | © The Author(s) 2018. Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| 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/10056086 |
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