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Multiscale convergence and reiterated homogenisation

Published online by Cambridge University Press:  14 November 2011

G. Allaire  and
M. Briane
G. Allaire
Affiliation:
Commissariat à l'Energie Atomique, DRN/DMT/SERMA, Centre d'Etudes de Saclay, 91191 Gif-sur-Yvette Cedex, France
M. Briane
Affiliation:
Département de Mathématiques, Université Paris 12, 61 ave. du Général de Gaulle, 94040 Créteil Cedex; Laboratoire d'Analyse Numérique, Tour 55-65-5ème étage, Université Paris 6, 4 place Jussieu, 75252 Paris Cedex 05, France
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Extract

This paper generalises the notion of two-scale convergence to the case of multiple separated scales of periodic oscillations. It allows us to introduce a multi-scale convergence method for the reiterated homogenisation of partial differential equations with oscillating coefficients. This new method is applied to a model problem with a finite or infinite number of microscopic scales, namely the homogenisation of the heat equation in a composite material. Finally, it is generalised to handle the homogenisation of the Neumann problem in a perforated domain.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 297 - 342
Copyright
Copyright © Royal Society of Edinburgh 1996

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