H⁰‐convergence and iterated homogenization

Article type: Research Article

Authors: Damlamian, A.^; | Donato, P.^;

Affiliations: Laboratoire d'Analyse et de Mathématiques Appliquées, CNRS UMR 8050, Universités de Marne‐la‐Vallée et Paris 12, Val‐de‐Marne, Université Paris 12, 94010 Créteil cedex, France E‐mail: damlamian@univ‐paris12.fr | Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, site Colbert, 76821 Mont Saint Aignan cedex, France E‐mails: donato@univ‐rouen.fr, donato@ann.jussieu.fr | Université Paris VI, Laboratoire Jacques‐Louis Lions, Boite courrier 187, 75252 Paris cedex, France

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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.

Journal: Asymptotic Analysis, vol. 39, no. 1, pp. 45-60, 2004