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Volume 28, Issue 3
Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients

Lin Wang, Ziqing Xie & Zhimin Zhang

DOI: 10.4208/jcm.2009.10-m1006

J. Comp. Math., 28 (2010), pp. 418-428.

Published online: 2010-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

Primary 65N30, Secondary 65N50, 65N15, 65N12, 65D10, 74S05, 41A10, 41A25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-418, author = {Lin Wang, Ziqing Xie and Zhimin Zhang}, title = {Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {3}, pages = {418--428}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1006}, url = {http://global-sci.org/intro/article_detail/jcm/8528.html} }
TY - JOUR T1 - Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients AU - Lin Wang, Ziqing Xie & Zhimin Zhang JO - Journal of Computational Mathematics VL - 3 SP - 418 EP - 428 PY - 2010 DA - 2010/06 SN - 28 DO - http://doi.org/10.4208/jcm.2009.10-m1006 UR - https://global-sci.org/intro/article_detail/jcm/8528.html KW - Eigenvalue, Spectral method, Collocation, Galerkin finite element method. AB -

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.

Lin Wang, Ziqing Xie and Zhimin Zhang. (2010). Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients. Journal of Computational Mathematics. 28 (3). 418-428. doi:10.4208/jcm.2009.10-m1006
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