Numerical approximation of the unique continuation problem enriched by a database for the Stokes equations
Year: 2025
Type: article
Abstract: 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.
DOI: 10.1051/m2an/2025024
Authors: Muriel Boulakia, Corrie James, Damiano Lombardi
Institutions: Centre National de la Recherche Scientifique, Université de Versailles Saint-Quentin-en-Yvelines, Université Paris-Saclay, Laboratoire de Mathématiques de Versailles, COMMEDIA: Mathématiques et calcul scientifique pour les applications bio-médicales, Institut national de recherche en sciences et technologies du numérique, Sorbonne Université, Laboratoire Jacques-Louis Lions
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid:
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4403116242