Computational unique continuation with finite dimensional Neumann trace
Numerical Analysis
2025-03-13 v2 Numerical Analysis
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 stabilised finite method.
Cite
@article{arxiv.2402.13695,
title = {Computational unique continuation with finite dimensional Neumann trace},
author = {Erik Burman and Lauri Oksanen and Ziyao Zhao},
journal= {arXiv preprint arXiv:2402.13695},
year = {2025}
}