On the heterogeneous multiscale method with various macroscopic solvers

doi:10.1016/j.na.2009.01.229

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	On the heterogeneous multiscale method with various macroscopic solvers
	Chen, Zhangxin
刊名	nonlinear analysis theory methods applications
	2009
关键词	Heterogeneous multiscale method Finite difference Finite element Discontinuous Galerkin Mixed finite element Nonconforming finite element Control volume finite element Mixed covolume Elliptic homogenization problem Nonlinear problems Random problems Convergence Stability Error estimate FINITE-ELEMENT-METHOD ELLIPTIC HOMOGENIZATION PROBLEMS CONVECTION-DIFFUSION PROBLEMS VOLUME METHODS QUADRILATERAL GRIDS GENERAL FRAMEWORK COVOLUME METHODS GALERKIN METHOD CONVERGENCE
DOI	10.1016/j.na.2009.01.229
英文摘要	The heterogeneous multiscale method (HMM) is a general method for efficient numerical solution of problems with multiscales. It consists of two components: an overall macroscopic solver for macrovariables on a macrogrid and an estimation of the missing macroscopic data from the microscopic model. In this paper we present a state-of-the-art review of the HMM with various macroscopic solvers, including finite differences, finite elements, discontinuous Galerkin, mixed finite elements, control volume finite elements, nonconforming finite elements, and mixed covolumes. The first four solvers have been studied in the HMM setting; the others are not. As example, the HMM with the nonconforming finite element macroscopic solver for nonlinear and random homogenization problems is also studied here. (C) 2009 Elsevier Ltd. All rights reserved.; Mathematics, Applied; Mathematics; SCI(E); EI; 2; ARTICLE; 7-8; 3267-3282; 71
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/154930]
专题	工学院
推荐引用方式 GB/T 7714	Chen, Zhangxin. On the heterogeneous multiscale method with various macroscopic solvers[J]. nonlinear analysis theory methods applications,2009.
APA	Chen, Zhangxin.(2009).On the heterogeneous multiscale method with various macroscopic solvers.nonlinear analysis theory methods applications.
MLA	Chen, Zhangxin."On the heterogeneous multiscale method with various macroscopic solvers".nonlinear analysis theory methods applications (2009).