Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems

doi:10.1515/JNUM.2010.003

	Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems
	Xu, X.1 ; Chen, H.1; Hoppe, R. H. W.2,3
	2010-04-01
发表期刊	JOURNAL OF NUMERICAL MATHEMATICS
ISSN	1570-2820
卷号	18 期号:1 页码:59-90
摘要	A local multilevel product algorithm and its additive version are analyzed for linear systems arising from the application of adaptive finite element methods to second order elliptic boundary value problems. The abstract Schwarz theory is applied to verify uniform convergence of local multilevel methods featuring Jacobi and Gauss-Seidel smoothing only on local nodes. By this abstract theory, convergence estimates can be further derived for the hierarchical basis multigrid method and the hierarchical basis preconditioning method on locally refined meshes, where local smoothing is performed only on new nodes. Numerical experiments confirm the optimality of the suggested algorithms.
关键词	local multilevel methods adaptive finite element methods local smoothing Schwarz theory optimality
DOI	10.1515/JNUM.2010.003
语种	英语
资助项目	National Basic Research Program of China[2005CB321701] ; National Natural Science Foundation of China[10731060] ; NSF[DMS-0707602] ; NSF[DMS-0810156] ; NSF[DMS-0811153] ; NSF[DMS-0914788]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000276911700003
出版者	WALTER DE GRUYTER & CO
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9898
专题	计算数学与科学工程计算研究所
通讯作者	Xu, X.
作者单位	1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Univ Houston, Dept Math, Houston, TX 77204 USA 3.Univ Augsburg, Inst Math, D-86159 Augsburg, Germany
推荐引用方式 GB/T 7714	Xu, X.,Chen, H.,Hoppe, R. H. W.. Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems[J]. JOURNAL OF NUMERICAL MATHEMATICS,2010,18(1):59-90.
APA	Xu, X.,Chen, H.,&Hoppe, R. H. W..(2010).Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems.JOURNAL OF NUMERICAL MATHEMATICS,18(1),59-90.
MLA	Xu, X.,et al."Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems".JOURNAL OF NUMERICAL MATHEMATICS 18.1(2010):59-90.