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A boundary-element method with mesh refinement for a weakly singular integral equation. (English) Zbl 0731.65119

A weakly singular integral equation of the first kind on an open, smooth surface piece \(\Gamma\) in \({\mathbb{R}}^ 3\) is solved approximately via the Galerkin method. The authors show how to compensate the effect of the edge singularities by using an appropriately graded mesh. Numerical experiments for the Galerkin method, using piecewise constant and piecewise linear functions on triangles, demonstrate the effect of graded meshes and show experimental rates of convergence which underline the theoretical results.
Reviewer: M.Schleiff (Halle)

MSC:

65R20 Numerical methods for integral equations
65N38 Boundary element methods for boundary value problems involving PDEs
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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