Spectral method with the tensor-product nodal basis for the Steklov eigenvalue problem (Q473935)

Summary: 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 \textit{J. M. Melenk} and \textit{B. I. Wohlmuth} [Adv. Comput. Math. 15, No. 1--4, 311--331 (2001; Zbl 0991.65111)], 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.