Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem

doi:10.1016/j.apnum.2010.12.007

	Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem
	Chen, Hongtao 1,2; Jia, Shanghui 3; Xie, Hehu1,4
	2011-04-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	61 期号:4 页码:615-629
摘要	In this paper, we propose a method to improve the convergence rate of the lowest order Raviart-Thomas mixed finite element approximations for the second order elliptic eigenvalue problem. Here, we prove a supercloseness result for the eigenfunction approximations and use a type of finite element postprocessing operator to construct an auxiliary source problem. Then solving the auxiliary additional source problem on an augmented mixed finite element space constructed by refining the mesh or by using the same mesh but increasing the order of corresponding mixed finite element space, we can increase the convergence order of the eigenpair approximation. This postprocessing method costs less computation than solving the eigenvalue problem on the finer mesh directly. Some numerical results are used to confirm the theoretical analysis. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
关键词	Second order elliptic eigenvalue problem Mixed finite element method Raviart-Thomas Rayleigh quotient formula Supercloseness Postprocessing
DOI	10.1016/j.apnum.2010.12.007
语种	英语
资助项目	National Science Foundation of China (NSFC)[NSFC 11001259] ; National Science Foundation of China (NSFC)[NSFC 11071265]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000287183700014
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11543
专题	计算数学与科学工程计算研究所
通讯作者	Xie, Hehu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China 3.Cent Univ Finance & Econ, Sch Appl Math, Beijing 100081, Peoples R China 4.Otto VonGuericke Univ Magdegurg, Inst Anal & Computat Math, D-39016 Magdeburg, Germany
推荐引用方式 GB/T 7714	Chen, Hongtao,Jia, Shanghui,Xie, Hehu. Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem[J]. APPLIED NUMERICAL MATHEMATICS,2011,61(4):615-629.
APA	Chen, Hongtao,Jia, Shanghui,&Xie, Hehu.(2011).Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem.APPLIED NUMERICAL MATHEMATICS,61(4),615-629.
MLA	Chen, Hongtao,et al."Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem".APPLIED NUMERICAL MATHEMATICS 61.4(2011):615-629.