Adaptive Wavelet BEM for Boundary Integral Equations: Theory and Numerical Experiments

Stephan Dahlke, Helmut Harbrecht, Manuela Utzinger, Markus Weimar

Type: Article

Publication Date: 2017-07-28

Citations: 8

DOI: https://doi.org/10.1080/01630563.2017.1359623

Abstract

We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in ℝ3. The corresponding operator equations are treated by 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 based on the Besov regularity of the exact solution.

Locations

Numerical Functional Analysis and Optimization - View
arXiv (Cornell University) - View - PDF
edoc (University of Basel) - View - PDF

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+	Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems	1994	Carlos E. Kenig
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+	Theory of Function Spaces III	2006	Hans Triebel
+ PDF Chat	An optimal adaptive wavelet method without coarsening of the iterands	2006	Gantumur Tsogtgerel Helmut Harbrecht Rob Stevenson
+ PDF Chat	Almost Diagonal Matrices and Besov-Type Spaces Based on Wavelet Expansions	2015	Markus Weimar
+	An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems	2006	Gantumur Tsogtgerel
+	The Inhomogeneous Dirichlet Problem in Lipschitz Domains	1995	David Jerison Carlos E. Kenig
+ PDF Chat	Wavelets with patchwise cancellation properties	2006	Helmut Harbrecht Rob Stevenson