The aim of this monograph is to describe the main concepts and recent-vances in
multiscale? nite element methods. This monograph is intended for …

The purpose of this book is to explain systematically and clearly many of the most important
techniques set forth in recent years for using weak convergence methods to study nonlinear …

The focus of this book is the large-scale statistical behavior of solutions of divergence-form
elliptic equations with random coefficients, which is closely related to the long-time …

On W1,p estimates for elliptic equations in divergence form Page 1 On W1,p Estimates for
Elliptic Equations in Divergence Form LA CAFFARELLI Department of Mathematics and …

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 …

R.–Nous présentons des résultats quantitatifs pour l'homogénéisation de
fonctionnelles intégrales uniformément convexes avec coefficients aléatoires sous …

Periodic Homogenization of Elliptic Systems Page 1 Operator Theory Advances and
Applications 269 Zhongwei Shen Periodic Homogenization of Elliptic Systems Page 2 Page 3 …

1.1 Background In the closure D of a bounded domain in R n, we consider a composite
media whose physical characteristics are smooth in the closures of subdomains Dm but …

The multiscale finite element method (MsFEM)[TY Hou, XH Wu, and Z. Cai, Math. Comp.,
1998, to appear; TY Hou and XH Wu, J. Comput. Phys., 134 (1997), pp. 169--189] has been …

These notes are devoted to the study of some problems related to shallow-water equations.
In particular, we will review results from derivations of shallow-water systems which depend …