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

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  • Xuqing Zhang
  • Yidu Yang
  • Hai Bi

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.

Suggested Citation

  • Xuqing Zhang & Yidu Yang & Hai Bi, 2013. "Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:650530
    DOI: 10.1155/2013/650530
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