Burman, E;
Nechita, M;
Oksanen, L;
(2018)
Unique continuation for the Helmholtz equation using stabilized finite element methods.
Journal des Mathematiques Pures et Appliquees
10.1016/j.matpur.2018.10.003.
(In press).
Preview |
Text
Burman_1-s2.0-S0021782418301582-main.pdf - Published Version Download (1MB) | Preview |
Abstract
In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity assumption on the geometry, the constants grow at most linearly in the wave number. Then these estimates are used to obtain error bounds for the finite element method that are explicit with respect to the wave number. Some numerical illustrations are given.
| Type: | Article |
|---|---|
| Title: | Unique continuation for the Helmholtz equation using stabilized finite element methods |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.matpur.2018.10.003 |
| Publisher version: | http://doi.org/10.1016/j.matpur.2018.10.003 |
| Language: | English |
| Additional information: | Copyright © The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed. |
| Keywords: | Helmholtz equation, Unique continuation, Finite element methods, Wave number explicit, Conditional Hölder stability |
| 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/10026887 |
Archive Staff Only
 |
View Item |
