Computing the lower and upper bounds of Laplace eigenvalue problem:by combining conforming and nonconforming finite element methods

作     者：LUO FuSheng LIN Qun XIE HeHu 

作者机构：LSECICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2012年第55卷第5期

页      面：1069-1082页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070102[理学-计算数学] 0802[工学-机械工程] 0701[理学-数学] 

基　　金：supported by National Science Foundations of China (Grant Nos. 11001259,11031006) Croucher Foundation of Hong Kong Baptist University 

主　　题：lower bound upper bound ECR EQ1ro t eigenvalue problem postprocessing 

摘      要：We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue *** using the special nonconforming finite elements,i.e.,enriched Crouzeix-Raviart element and extended Q1ro t,we get the lower bound of the ***,we use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue,which only needs to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is ***,we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only *** numerical results are also presented to demonstrate our theoretical analysis.