Local inverse estimates for non-local boundary integral operators
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- by M. Aurada, M. Feischl, T. Führer, M. Karkulik, J. M. Melenk and D. Praetorius;
- Math. Comp. 86 (2017), 2651-2686
- 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.References
Bibliographic Information
- M. Aurada
- Affiliation: Technische Universität Wien, Institute for Analysis and Scientific Computing, Wiedner Haupstrasse 8-10-A, 1040 Vienna, Austria
- MR Author ID: 965857
- Email: markus.aurada@chello.at
- M. Feischl
- Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
- MR Author ID: 965785
- Email: m.feischl@unsw.edu.au
- T. Führer
- Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile
- MR Author ID: 1017746
- Email: tofuhrer@mat.puc.cl
- M. Karkulik
- Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
- MR Author ID: 965821
- 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
- MR Author ID: 613978
- ORCID: 0000-0001-9024-6028
- 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
- MR Author ID: 702616
- ORCID: 0000-0002-1977-9830
- Email: dirk.praetorius@tuwien.ac.at
- 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.
- © Copyright 2017 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 2651-2686
- MSC (2010): Primary 65J05, 65R20, 65N38
- DOI: https://doi.org/10.1090/mcom/3175
- MathSciNet review: 3667020