Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients

Authors

  • Lin Wang, Ziqing Xie & Zhimin Zhang

DOI:

https://doi.org/10.4208/jcm.2009.10-m1006

Keywords:

Eigenvalue, Spectral method, Collocation, Galerkin finite element method.

Abstract

We propose and analyze a $C^0$ spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.

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Published

2018-08-22

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  • 3575

Issue

Vol. 28 No. 3 (2010)

Section

Articles

How to Cite

Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients. (2018). Journal of Computational Mathematics, 28(3), 418-428. https://doi.org/10.4208/jcm.2009.10-m1006