| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1399 - 1435 | |
| DOI | https://doi.org/10.1051/m2an/2025024 | |
| Published online | 27 May 2025 | |
Numerical approximation of the unique continuation problem enriched by a database for the Stokes equations
1
Université Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, 78000 Versailles, France
2
Sorbonne Université, Inria and CNRS, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, France
* Corresponding author: corrie.james@inria.fr
Received:
4
October
2024
Accepted:
29
March
2025
This paper studies the unique continuation problem for the Stokes equations given a database of population measurements. The problem is set up as a minimization problem under a PDE constraint and discretized using the finite element method. It is then regularized by the population data, by imposing that the solution lives near a finite-dimensional subspace generated by the database. This study examines how the inclusion of population data in the resolution improves both theoretical and numerical results. Using the proposed method, global error estimates for the velocity and pressure are obtained at an improved rate of convergence. The inclusion of the population data also has a positive impact on the numerical test cases, in both 2D and 3D, and especially when the measurements are scarce.
Mathematics Subject Classification: 35R30 / 65N20 / 65N21 / 76M21
Key words: Data assimilation / unique continuation / Stokes
© The authors. Published by EDP Sciences, SMAI 2025
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 use, distribution, and reproduction in any medium, provided the original work is properly cited.
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