Boundary element approximation of Steklov eigenvalue problem for Helmholtz equation. (English) Zbl 0977.65100
Summary: The Steklov eigenvalue problem of Helmholtz equation is considered. The Steklov eigenvalue problem is reduced to a new variational formula on the boundary of a given domain, in which the selfadjoint property of the original differential operator is kept and the calculating of hyper-singular integral is avoided. A numerical example showing the efficiency of this method and an optimal error estimate are given.
MSC:
65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35P15 | Estimates of eigenvalues in context of PDEs |
65N38 | Boundary element methods for boundary value problems involving PDEs |