各向异性网格下特征值问题的有限元分析  

Analysis by Finite Element Methods for Eigenvalue Problems on Anisotropic Meshes

作　　者：彭玉成[1] 石东洋[1] 陈绍春[1] 

机构地区：[1]郑州大学数学系,河南郑州450052

出　　处：《数学的实践与认识》2006年第7期300-309,共10页Mathematics in Practice and Theory

基　　金：由国家自然科学基金(10371113;10471133);河南省自然科学基金(0611053100);河南省教委自然科学基金(2006110011)

摘　　要：主要目的是在各向异性网格下研究二阶椭圆特征值问题的两类非协调有限元—类Wilson矩形元和Carey三角形元—的收敛性分析.通过新的技巧和方法,得到了与传统有限元网格剖分下相同的特征对的最优误差估计.推广了已有的结果.In this paper the main interest is that the error estimates of the second order elliptic eigenvalue problems are studied by two kinds of nonconforming finite elements, Quasi-Wilson rectangular element and Carey triangular element, on anisotrepic meshes. By using the new techniques, the convergence analysis is presented and the optimal error estimates of eigenpair are obtained. The results of this paper can be regarded as a generalization to previous works. Thus the applicable scope of finite element methods is enlarged.

关 键 词：特征值问题 类WILSON元 Carey元 各向异性网格 最优误差估计 

分 类 号：O241.82[理学—计算数学]