| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2385 - 2413 | |
| DOI | https://doi.org/10.1051/m2an/2025060 | |
| Published online | 17 September 2025 | |
Solving the unique continuation problem for Schrödinger equations with low regularity solutions using a stabilized finite element method
1
Department of Mathematics, University College London, London, UK
2
Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
14
May
2024
Accepted:
24
June
2025
Abstract
In this paper, we consider the unique continuation problem for the Schrödinger equations. We prove a Hölder type conditional stability estimate and build up a parameterized stabilized finite element scheme adaptive to the a priori knowledge of the solution, achieving error estimates in interior domains with convergence up to continuous stability. The approximability of the scheme to solutions with regularity of as low as H1 is studied and the convergence rates for discrete solutions under L2 and H1 norms are shown. Comparisons in terms of different parameterization for different regularities will be illustrated with respect to the convergence and condition numbers of the linear systems. Finally, numerical experiments will be given to illustrate the theory.
Mathematics Subject Classification: 65N12 / 65N20
Key words: Unique continuation / Schrödinger equations / finite element / low regularity
© The authors. Published by EDP Sciences, SMAI 2025
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