A mixed multiscale finite element method for elliptic problems with oscillating coefficients

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	A mixed multiscale finite element method for elliptic problems with oscillating coefficients
	Chen, ZM ; Hou, TY
	2003
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	72 期号:242 页码:541-576
摘要	The recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large-scale structure of the solutions without resolving all the fine-scale structures. Motivated by the numerical simulation of flow transport in highly heterogeneous porous media, we propose a mixed multiscale finite element method with an over-sampling technique for solving second order elliptic equations with rapidly oscillating coefficients. The multiscale finite element bases are constructed by locally solving Neumann boundary value problems. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for flow transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000180911800002
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18320
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, ZM
作者单位	1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100080, Peoples R China 2.CALTECH, Pasadena, CA 91125 USA
推荐引用方式 GB/T 7714	Chen, ZM,Hou, TY. A mixed multiscale finite element method for elliptic problems with oscillating coefficients[J]. MATHEMATICS OF COMPUTATION,2003,72(242):541-576.
APA	Chen, ZM,&Hou, TY.(2003).A mixed multiscale finite element method for elliptic problems with oscillating coefficients.MATHEMATICS OF COMPUTATION,72(242),541-576.
MLA	Chen, ZM,et al."A mixed multiscale finite element method for elliptic problems with oscillating coefficients".MATHEMATICS OF COMPUTATION 72.242(2003):541-576.