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A boundary element Galerkin method for a hypersingular integral equation on open surfaces

✍ Scribed by V. J. Ervin; E. P. Stephan

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
403 KB
Volume
13
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

A hypersingular boundary integral equation of the first kind on an open surface piece Ξ“ is solved approximately using the Galerkin method. As boundary elements on rectangles we use continuous, piecewise bilinear functions which vanish on the boundary of Ξ“. We show how to compensate for the effect of the edge and corner singularities of the true solution of the integral equation by using an appropriately graded mesh and obtain the same convergence rate as for the case of a smooth solution. We also derive asymptotic error estimates in lower‐order Sobolev norms via the Aubin–Nitsche trick. Numerical experiments for the Galerkin method with piecewise linear functions on triangles demonstrate the effect of graded meshes and show experimental rates of convergence which underline the theoretical results.

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