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S. Kurz, D. Pauly, D. Praetorius, S. Repin, D. Sebastian:
"Functional a posteriori error estimates for boundary element methods";
in: "ASC Report 29/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 29.

Functional error estimates are well-estabilished 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 as well as collocation, which makes our approach of particular interest for people working in engineering. Numerical experiments for the Laplace problem confirm the theoretical results.

boundary element method, functional a posteriori error estimate, adaptive mesh-refinement.

http://www.asc.tuwien.ac.at/preprint/2019/asc29x2019.pdf