## 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