Eigenvalue approximation from below using non-conforming finite elements

查看全文 作　　者：YANG YiDu 1 ,ZHANG ZhiMin 2 & LIN FuBiao 11 School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China;2 Department of Mathematics,Wayne State University,Detroit,MI 48202,USA

出　　处：《Science China Mathematics》索引2010年第53卷第1期,共14页

基　　金：supported by National Natural Science Foundation of China (Grant No.10761003);the US National Science Foundation(Grant No. DMS-0612908) 摘　　要：This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems. 关键词：non-conforming ELEMENT EIGENVALUE LOWER BOUND

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Eigenvalue approximation from below using non-conforming finite elements

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