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
Source Publication	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
Volume	35 Issue:4 Pages:1888-1912
Abstract	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.
Keyword	multigrid method jump coefficient problem discrete harmonic extension nearly singular problem preconditioned conjugate gradient method
DOI	10.1093/imanum/dru055
Language	英语
Funding Project	National Science Foundation of China (NSFC)[10971006] ; National Science Foundation of China (NSFC)[91130011] ; NSFC[91130001] ; NSFC[11421101]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000362826000015
Publisher	OXFORD UNIV PRESS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/21011
Collection	中国科学院数学与系统科学研究院
Corresponding Author	Wu, Jinbiao
Affiliation	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
Recommended Citation 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.

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