Bespalov, A;
Betcke, T;
Haberl, A;
Praetorius, D;
(2019)
Adaptive BEM with optimal convergence rates for the Helmholtz equation.
Computer Methods in Applied Mechanics and Engineering
, 346
pp. 260-287.
10.1016/j.cma.2018.12.006.
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Abstract
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation.
| Type: | Article |
|---|---|
| Title: | Adaptive BEM with optimal convergence rates for the Helmholtz equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2018.12.006 |
| Publisher version: | https://doi.org/10.1016/j.cma.2018.12.006 |
| 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: | Boundary element method, Helmholtz equation, A posteriori error estimate, Adaptive algorithm, Convergence, Optimality |
| 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/10065933 |
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