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Caccioppoli-type estimates and $\mathcal{H}$-Matrix approximations to inverses for FEM-BEM couplings (2008.11498v1)
Published 26 Aug 2020 in math.NA and cs.NA
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.