Burman, Erik;
Nechita, Mihai;
Oksanen, Lauri;
(2024)
Optimal Approximation of Unique Continuation.
Foundations of Computational Mathematics
10.1007/s10208-024-09655-w.
(In press).
Preview |
Text
Burman_s10208-024-09655-w.pdf Download (509kB) | Preview |
Abstract
We consider numerical approximations of ill-posed elliptic problems with conditional stability. The notion of optimal error estimates is defined including both convergence with respect to discretisation and perturbations in data. The rate of convergence is determined by the conditional stability of the underlying continuous problem and the polynomial order of the approximation space. A proof is given that no approximation can converge at a better rate than that given by the definition without increasing the sensitivity to perturbations, thus justifying the concept. A recently introduced class of primal-dual finite element methods with weakly consistent regularisation is recalled and the associated error estimates are shown to be optimal in the sense of this definition.
| Type: | Article |
|---|---|
| Title: | Optimal Approximation of Unique Continuation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10208-024-09655-w |
| Publisher version: | http://dx.doi.org/10.1007/s10208-024-09655-w |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Unique continuation; Ill-posed problems; Conditional stability; Approximation methods; Finite element methods; Stabilised methods; Regularisation; Error estimates; Optimality; Optimal convergence |
| 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-pp.ucl.ac.uk/id/eprint/10192980 |
Archive Staff Only
 |
View Item |
