Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings
Numerical Analysis
2024-07-25 v1 Numerical Analysis
Abstract
We consider three different methods for the coupling of the finite element method and the boundary element method, the Bielak-MacCamy coupling, the symmetric coupling, and the Johnson-N\'ed\'elec coupling. For each coupling we provide discrete interior regularity estimates. As a consequence, we are able to prove the existence of exponentially convergent -matrix approximants to the inverse matrices corresponding to the lowest order Galerkin discretizations of the couplings.
Keywords
Cite
@article{arxiv.2008.11498,
title = {Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings},
author = {Markus Faustmann and Jens Markus Melenk and Maryam Parvizi},
journal= {arXiv preprint arXiv:2008.11498},
year = {2024}
}