A Nystrom method for a boundary integral equation related to the Dirichlet problem on domains with corners

Abstract

The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of Nystrom type, based on a Lobatto quadrature rule.The convergence and stability of the method are proved and some numerical tests are included.