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

文献类型：期刊论文

作者Chen, Hongtao1,2; Jia, Shanghui3; Xie, Hehu1,4
刊名APPLIED NUMERICAL MATHEMATICS
出版日期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
DOI10.1016/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
WOS记录号WOS:000287183700014
出版者ELSEVIER SCIENCE BV
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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