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 - <p style="text-align: justify;">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.</p>