H 0 ‐convergence and iterated homogenization

Abstract

In this paper we give a general iterative method for the homogenization of elliptic problems in perforated domains with finitely many periodic scales. It is derived from a more general result, where only one (the biggest) scale is assumed to be ε‐periodic. For the smaller scales, only H⁰‐convergence is assumed. In the case of finitely many periodic scales, explicit formulas for the homogenized operators are obtained.