Functional a posteriori error estimates for boundary element methods
Abstract
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202103242077Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0029-599X
DOI
https://doi.org/10.1007/s00211-021-01188-6
Language
English
Published in
Numerische Mathematik
Citation
- Kurz, S., Pauly, D., Praetorius, D., Repin, S., & Sebastian, D. (2021). Functional a posteriori error estimates for boundary element methods. Numerische Mathematik, 147(4), 937-966. https://doi.org/10.1007/s00211-021-01188-6
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Additional information about funding
D. Sebastian and D. Praetorius thankfully acknowledge support by the Austrian Science Fund (FWF) through the SFB Taming complexity in partial differential systems, and the stand-alone project Optimal adaptivity for BEM and FEM-BEM coupling (grant P27005). The work of S. Kurz was supported in part by the Excellence Initiative of the German Federal and State Governments, and in part by the Graduate School of Computational Engineering at TU Darmstadt.
Copyright© The Author(s) 2021