Burman, Erik;
Oksanen, Lauri;
Zhao, Ziyao;
(2025)
Computational Unique Continuation with Finite Dimensional Neumann Trace.
SIAM Journal on Numerical Analysis
, 63
(5)
pp. 1986-2008.
10.1137/24m164080x.
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Abstract
We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative error estimates we prove Lipschitz stability of the unique continuation problem in the global H1 -norm. This stability is then leveraged to derive optimal a posteriori and a priori error estimates for a primal-dual stabilized finite element method.
| Type: | Article |
|---|---|
| Title: | Computational Unique Continuation with Finite Dimensional Neumann Trace |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/24m164080x |
| Publisher version: | https://doi.org/10.1137/24m164080x |
| 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: | Unique continuation; conditional stability; finite dimension; Neumann boundary; finite element methods; 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/10214704 |
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