E, Weinan; Ming, Pingbing Analysis of multiscale methods. (English) Zbl 1046.65108 J. Comput. Math. 22, No. 2, 210-219 (2004). Summary: The heterogeneous multiscale method gives a general framework for the analysis of multiscale methods. In this paper, we demonstrate this by applying this framework to two canonical problems: The elliptic problem with multiscale coefficients and the quasicontinuum method. Cited in 10 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74N05 Crystals in solids Keywords:multigrid method; finite element method; homogenization; crystal; quasicontinuum method; multiscale method; elliptic problem PDF BibTeX XML Cite \textit{W. E} and \textit{P. Ming}, J. Comput. Math. 22, No. 2, 210--219 (2004; Zbl 1046.65108)