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

doi:10.1016/j.apnum.2010.12.007

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	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
刊名	APPLIED NUMERICAL MATHEMATICS
	2011-04-01
卷号	61 期号:4 页码:615-629
关键词	Second order elliptic eigenvalue problem Mixed finite element method Raviart-Thomas Rayleigh quotient formula Supercloseness Postprocessing
ISSN号	0168-9274
DOI	10.1016/j.apnum.2010.12.007
英文摘要	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.
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
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000287183700014
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/11542]
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.