Burman, E;
Hansbo, P;
Larson, MG;
Massing, A;
(2020)
A stable cut finite element method for partial differential equations on surfaces: The Helmholtz–Beltrami operator.
Computer Methods in Applied Mechanics and Engineering
, 362
, Article 112803. 10.1016/j.cma.2019.112803.
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Abstract
We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. Using a stabilized method combining Galerkin least squares stabilization and a penalty on the gradient jumps we obtain stability of the discrete formulation under the condition hk<C, where h denotes the mesh size, k the wave number and C a constant depending mainly on the surface curvature κ, but not on the surface/mesh intersection. Optimal error estimates in the H1 and L2-norms follow.
| Type: | Article |
|---|---|
| Title: | A stable cut finite element method for partial differential equations on surfaces: The Helmholtz–Beltrami operator |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2019.112803 |
| Publisher version: | https://doi.org/10.1016/j.cma.2019.112803 |
| Language: | English |
| Additional information: | Helmholtz-Beltrami, TraceFEM, stabilization |
| 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.ucl.ac.uk/id/eprint/10090691 |
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