Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

Abstract EN

This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem.

A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001), a posterior error estimator of the residual type is given and analyzed.

In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme.

Finally, numerical experiments with MATLAB program are reported.