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Mathematical Problems in Engineering
Volume 2013, Article ID 650530, 9 pages
http://dx.doi.org/10.1155/2013/650530
Research Article

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

School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received 18 January 2013; Accepted 3 September 2013

Academic Editor: Daoyi Dong

Copyright © 2013 Xuqing Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.