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The Dual Singular Function Method for 2D Boundary Integral Equations

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Abstract

The accuracy of standard boundary element methods for elliptic boundary value problems deteriorates if the boundary of the domain contains corners or if the boundary conditions change along the boundary. Here we first investigate the convergence behaviour of standard spline Galerkin approximation on quasi-uniform meshes for boundary integral equations on polygonal domains. It turns out, that the order of convergence depends on some constant describing the singular behaviour of solutions near corner points of the boundary. In order to recover the full order of convergence for the Galerkin approximation we propose the dual singular function method which is often used for improving the accuracy of finite element methods. The theoretical convergence results are confirmed and illustrated by a numerical example.

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  1. Abteilung Analysis, Universität Ulm, 89077, Ulm, Germany

    Marius Bochniak

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  1. Marius Bochniak
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Bochniak, M. The Dual Singular Function Method for 2D Boundary Integral Equations. Advances in Computational Mathematics 20, 293–310 (2004). https://doi.org/10.1023/A:1027370428226

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