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M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
"Local inverse estimates for non-local boundary integral operators";
in: "ASC Report 12/2015", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2015, ISBN: 978-3-902627-08-7, 1 - 28.

We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded Lipschitz domain $\Omega$ in $\bf R^d$ for $d ≥ 2$ with piecewise smooth boundary. For piecewise polynomial ansatz spaces and $d \in \{2,3\}$, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to effciency estimates in a posteriori error estimation in boundary element methods is given.

boundary element method; inverse estimates; hp-finite element spaces.

http://www.asc.tuwien.ac.at/preprint/2015/asc12x2015.pdf