Functional a posteriori error estimates for boundary element methods
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
Published inNumerische Mathematik
© The Author(s) 2021
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.
ISSN Search the Publication Forum0029-599X
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Additional information about fundingD. 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. ...
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