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Local inverse estimates for non-local boundary integral operators


Authors: M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. M. Melenk and D. Praetorius
Journal: Math. Comp.
MSC (2010): Primary 65J05, 65R20, 65N38
DOI: https://doi.org/10.1090/mcom/3175
Published electronically: April 28, 2017
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Abstract: 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 $ \mathbb{R}^d$ for $ d\ge 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 efficiency-type estimates in a posteriori error estimation in boundary element methods is given.


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Additional Information

M. Aurada
Affiliation: Technische Universität Wien, Institute for Analysis and Scientific Computing, Wiedner Haupstrasse 8-10-A, 1040 Vienna, Austria
Email: markus.aurada@chello.at

M. Feischl
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
Email: m.feischl@unsw.edu.au

T. Führer
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile
Email: tofuhrer@mat.puc.cl

M. Karkulik
Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
Email: michael.karkulik@usm.cl

J. M. Melenk
Affiliation: Technische Universität Wien, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
Email: melenk@tuwien.ac.at

D. Praetorius
Affiliation: Technische Universität Wien, Institute for Analysis and Scientific Computing, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria
Email: dirk.praetorius@tuwien.ac.at

DOI: https://doi.org/10.1090/mcom/3175
Keywords: Boundary element method, inverse estimates, adaptivity, efficiency, $hp$-finite element spaces
Received by editor(s): April 16, 2015
Received by editor(s) in revised form: February 19, 2016
Published electronically: April 28, 2017
Additional Notes: The second and sixth authors were supported by the Austrian Science Fund (FWF) under grant P27005. The second, fifth, and sixth authors were supported through the FWF doctoral school W124. The third author was supported by CONICYT through FONDECYT project 3150012. The fourth author was supported by CONICYT through FONDECYT project 3140614 and by NSF under grant DMS-1318916.
Article copyright: © Copyright 2017 American Mathematical Society