A refined convergence analysis of multigrid algorithms for elliptic equations

doi:10.1142/S0219530514500080

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	A refined convergence analysis of multigrid algorithms for elliptic equations
	Chang, Qianshun 1,2; Jia, Rong-Qing 3
	2015-05-01
发表期刊	ANALYSIS AND APPLICATIONS
ISSN	0219-5305
卷号	13 期号:3 页码:255-290
摘要	Multigrid algorithms, in particular, multigrid V-cycles, are investigated in this paper. We establish a general theory for convergence of the multigrid algorithm under certain approximation conditions and smoothing conditions. Our smoothing conditions are satisfied by commonly used smoothing operators including the standard Gauss-Seidel method. Our approximation conditions are verified for finite element approximation to numerical solutions of elliptic partial differential equations without any requirement of additional regularity of the solution. Our convergence analysis of multigrid algorithms can be applied to a wide range of problems. Numerical examples are also provided to illustrate the general theory.
关键词	Multigrid algorithms elliptic equations multilevel approximation approximation conditions smoothing conditions finite element approximation
DOI	10.1142/S0219530514500080
语种	英语
资助项目	PAPD of Jiangsu Higher Education Institutions ; NSERC Canada[OGP 121336]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000355453400002
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19862
专题	中国科学院数学与系统科学研究院
通讯作者	Chang, Qianshun
作者单位	1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
推荐引用方式 GB/T 7714	Chang, Qianshun,Jia, Rong-Qing. A refined convergence analysis of multigrid algorithms for elliptic equations[J]. ANALYSIS AND APPLICATIONS,2015,13(3):255-290.
APA	Chang, Qianshun,&Jia, Rong-Qing.(2015).A refined convergence analysis of multigrid algorithms for elliptic equations.ANALYSIS AND APPLICATIONS,13(3),255-290.
MLA	Chang, Qianshun,et al."A refined convergence analysis of multigrid algorithms for elliptic equations".ANALYSIS AND APPLICATIONS 13.3(2015):255-290.