Burman, Erik;
Hansbo, Peter;
Larson, Mats G;
(2022)
Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension.
SIAM Journal on Scientific Computing
, 44
(3)
A1254-A1289.
10.1137/20m137937x.
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Abstract
In this paper we develop a fully explicit cut finite element method for the wave equation. The method is based on using a standard leap frog scheme combined with an extension operator that defines the nodal values outside of the domain in terms of the nodal values inside the domain. We show that the mass matrix associated with the extended finite element space can be lumped leading to a fully explicit scheme. We derive stability estimates for the method and provide optimal order a priori error estimates. Finally, we present some illustrating numerical examples.
| Type: | Article |
|---|---|
| Title: | Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/20m137937x |
| Publisher version: | https://doi.org/10.1137/20M137937X |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | wave equation, explicit time stepping, CutFEM, discrete extension operator, a priori error estimates |
| 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/10149178 |
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