The solution of Laplacian problems over L‐shaped domains with a singular function boundary integral method

Abstract

Abstract The singular function boundary integral method is applied for the solution of a Laplace equation problem over an L‐shaped domain. The solution is approximated by the leading terms of the local asymptotic solution expansion, while the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. Estimates of great accuracy are obtained for the leading singular coefficients, as well as for the Lagrange multipliers. Comparisons are made with recent numerical results in the literature. Copyright © 2002 John Wiley & Sons, Ltd.