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New application of hypersingular equations in the boundary element method. (English) Zbl 0766.65091

The authors propose a new method of dealing Dirichlet corners and star points with a collocation based boundary element method (BEM). They supplement an appropriate number of discretized derivatives of boundary integral equations to the standard BEM scheme to obtain the same number of equations as unknowns. A method of calculating the hypersingular integrals is described and some numerical examples are given.
Reviewer: G.Schmidt (Berlin)

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
74S15 Boundary element methods applied to problems in solid mechanics
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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