Burman, Erik;
Oksanen, Lauri;
(2024)
Finite element approximation of unique continuation of functions with finite dimensional trace.
Mathematical Models and Methods in Applied Sciences
10.1142/s0218202524500362.
(In press).
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Abstract
We consider a unique continuation problem where the Dirichlet trace of the solution is known to have finite dimension. We prove Lipschitz stability of the unique continuation problem and design a finite element method that exploits the finite dimensionality to enhance stability. Optimal a priori and a posteriori error estimates are shown for the method. The extension to problems where the trace is not in a finite dimensional space, but can be approximated to high accuracy using finite dimensional functions is discussed. Finally, the theory is illustrated in some numerical examples.
| Type: | Article |
|---|---|
| Title: | Finite element approximation of unique continuation of functions with finite dimensional trace |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1142/s0218202524500362 |
| Publisher version: | http://dx.doi.org/10.1142/s0218202524500362 |
| Language: | English |
| Additional information: | Copyright © The Author(s) Open Access since August 2024. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License, https://creativecommons.org/licenses/by/4.0/, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Unique continuation; finite element method; Lipschitz stability; stabilized methods; error estimates |
| 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/10196114 |
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