The Eigenvalue Approximations of the Laplace Operator Defined on a Domain with Strongly Deformed Boundary

Abstract

In this paper the eigenvalue approximations of the Laplace operator defined on a domain with strongly deformed boundary are presented. Because the exact eigenfunctions exhibit complicated behaviour in the vicinity of singular points of the used conformal mapping, the B-spline trial functions are used in order to improve the quality of the eigenfunction approximations near the singular points.