Burman, Erik;
Preuss, Janosch;
(2025)
Unique continuation for the wave equation based on a discontinuous Galerkin time discretization.
IMA Journal of Numerical Analysis
, Article draf036. 10.1093/imanum/draf036.
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Abstract
We consider a stable unique continuation problem for the wave equation that has been discretized so far using fairly sophisticated space-time methods. Here, we propose to solve this problem using a standard discontinuous Galerkin method for the temporal discretization. Error estimates are established under a geometric control condition. We also investigate two preconditioning strategies that can be used to solve the arising globally coupled space-time system by means of simple time-stepping procedures. Our numerical experiments test the performance of these strategies and highlight the importance of the geometric control condition for reconstructing the solution beyond the data domain.
| Type: | Article |
|---|---|
| Title: | Unique continuation for the wave equation based on a discontinuous Galerkin time discretization |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imanum/draf036 |
| Publisher version: | https://doi.org/10.1093/imanum/draf036 |
| Language: | English |
| Additional information: | © The Author(s) 2025. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, unique continuation, data assimilation, wave equation, finite-element method, discontinuous Galerkin, preconditioning, geometric control condition, FINITE-ELEMENT METHODS, CAUCHY-PROBLEM, OBSERVABILITY, SEMIDISCRETE, PROPAGATION, TOMOGRAPHY |
| 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/10211254 |
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