Error Analysis for the BEM on Nonsmooth Curves

  • T. Hartmann
  • E. P. Stephan
Conference paper

Abstract

In the following several methods for approximating the solution of integral equations on polygons are considered. These methods and the techniques of proving stability and error estimates have to take care of the fact that the solutions of the equations considered contain singularities. In Section 2 we derive stability conditions for a quadrature method using splines for a weakly singular integral equation. The same equation is considered in the next two sections. In Section 3 collocation methods using Jacobi weights and polynomials were extended from an interval to a polygon and in Section 4, local error estimates for Galerkin’s method are given. In Section 5 a discrete collocation method using a nonlinear transform is considered for solving a hypersingular integral equation.

Keywords

Convolution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • T. Hartmann
  • E. P. Stephan

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