SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS  

作　　者：Lin Wang Ziqing Xie Zhimin Zhang 

机构地区：[1]College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China and College of Information Technical Science, Nankai University, Tianjin 300071, China [2]College of Mathematics and Computer Science, Hunan Normal University, Changsha 310081, China [3]Department of Mathematics, Wayne State University, Detroit, MI 48202, USA and College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China

出　　处：《Journal of Computational Mathematics》2010年第3期418-428,共11页计算数学（英文）

基　　金：supported in part by the Programme for New Century Excellent Talents in University (NCET-06-0712);the National Natural Science Foundation of China (NSFC 10871066, 10571053);Key Laboratory of High Performance Computing and Stochastic Information Processing, Ministry of Education of China, Hunan Normal University;supported in part by the US National Science Foundation grant DMS-0612908

摘　　要：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.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.

关 键 词：EIGENVALUE Spectral method COLLOCATION Galerkin finite element method. 

分 类 号：O241.6[理学—计算数学] O241.82[理学—数学]