Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients

doi:10.1093/imanum/dru055

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	Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients
	Zheng, Hui 1; Wu, Jinbiao 2
	2015-10-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	35 期号:4 页码:1888-1912
摘要	In this paper, we investigate the multigrid methods for the linear finite element approximation of elliptic problems with large jumps in coefficients. Some singular functions, which cause the deterioration of the convergence rate, are introduced in our space splitting. According to the space splitting, we construct a modified multigrid method and prove that its uniform convergence is independent of the mesh size and the jumps. As a result, we also prove that the conjugate gradient method with the 'V'-cycle multigrid preconditioner converges uniformly.
关键词	multigrid method jump coefficient problem discrete harmonic extension nearly singular problem preconditioned conjugate gradient method
DOI	10.1093/imanum/dru055
语种	英语
资助项目	National Science Foundation of China (NSFC)[10971006] ; National Science Foundation of China (NSFC)[91130011] ; NSFC[91130001] ; NSFC[11421101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000362826000015
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21011
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Jinbiao
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Peking Univ, Sch Math Sci, HEDPS, CAPT & LMAM, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Zheng, Hui,Wu, Jinbiao. Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2015,35(4):1888-1912.
APA	Zheng, Hui,&Wu, Jinbiao.(2015).Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients.IMA JOURNAL OF NUMERICAL ANALYSIS,35(4),1888-1912.
MLA	Zheng, Hui,et al."Convergence analysis on multigrid methods for elliptic problems with large jumps in coefficients".IMA JOURNAL OF NUMERICAL ANALYSIS 35.4(2015):1888-1912.