Numerical methods for multiscale elliptic problems

doi:10.1016/j.jcp.2005.09.024

	Numerical methods for multiscale elliptic problems
	Ming, PB; Yue, XY
	2006-05-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	214 期号:1 页码:421-445
摘要	We present an overview of the recent development on numerical methods for elliptic problems with multiscale coefficients. We carry out a thorough study of two representative techniques: the heterogeneous multiscale method (HMM) and the multiscale finite element method (MsFEM). For problems with scale separation (but without specific assumptions on the particular form of the coefficients), analytical and numerical results show that HMM gives comparable accuracy as MsFEM, with much less cost. For problems without scale separation, our numerical results suggest that HMM performs at least as well as MsFEM, in terms of accuracy and cost, even though in this case both methods may fail to converge. Since the cost of MsFEM is comparable to that of solving the full fine scale problem, one might expect that it does not need scale separation and still retains some accuracy. We show that this is not the case. Specifically, we give an example showing that if there exists an intermediate scale comparable to H, the size of the macroscale mesh, then MsFEM commits a finite error even with overlapping. (c) 2005 Elsevier Inc. All rights reserved.
关键词	heterogeneous multiscale method multiscale finite element method scale separation
DOI	10.1016/j.jcp.2005.09.024
语种	英语
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000236417400021
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3510
专题	计算数学与科学工程计算研究所
通讯作者	Ming, PB
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, AMSS, Beijing 100080, Peoples R China 2.Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China
推荐引用方式 GB/T 7714	Ming, PB,Yue, XY. Numerical methods for multiscale elliptic problems[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2006,214(1):421-445.
APA	Ming, PB,&Yue, XY.(2006).Numerical methods for multiscale elliptic problems.JOURNAL OF COMPUTATIONAL PHYSICS,214(1),421-445.
MLA	Ming, PB,et al."Numerical methods for multiscale elliptic problems".JOURNAL OF COMPUTATIONAL PHYSICS 214.1(2006):421-445.