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arXiv · 2008.11498

Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings

Markus Faustmann·Jens Markus Melenk·Maryam Parvizi
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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 $\mathcal{H}$-matrix approximants to the inverse matrices corresponding to the lowest order Galerkin discretizations of the couplings.

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Markus Faustmann, Jens Markus Melenk, Maryam Parvizi. 2020-08-26. Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings. https://doi.org/10.1007/s00211-021-01261-0

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