# Adaptive Wavelet BEM for boundary integral equations. Theory and numerical experiments

Dahlke, Stephan and Harbrecht, Helmut and Utzinger, Manuela and Weimar, Markus. (2016) Adaptive Wavelet BEM for boundary integral equations. Theory and numerical experiments. Preprints Fachbereich Mathematik, 2016 (20).

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## Abstract

In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in $\mathbb{R}^3$. The corresponding operator equations are treated by means of adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions that can be made on the basis of a systematic investigation of the Besov regularity of the exact solution.
Faculties and Departments: 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)12 Special Collections > Preprints Fachbereich Mathematik Harbrecht, Helmut and Utzinger, Manuela Preprint Universität Basel English 10.5451/unibas-ep69953 21 Apr 2019 22:19 28 Mar 2019 09:51

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