Convergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem

Abstract

In this paper, a rigorous convergence and error analysis of a Galerkin boundary element method for the Dirichlet Laplacian eigenvalue problem is presented. The formulation of the eigenvalue problem in terms of a boundary integral equation yields a nonlinear boundary integral operator eigenvalue problem. This nonlinear eigenvalue problem and its Galerkin approximation are analyzed in the framework of eigenvalue problems for holomorphic Fredholm operator-valued functions. The convergence of the approximation is shown and quasi-optimal error estimates are presented. Numerical experiments are given confirming the theoretical results.