Multiscale convergence and reiterated homogenisation
- 1 January 1996
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 126 (2) , 297-342
- https://doi.org/10.1017/s0308210500022757
Abstract
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.Keywords
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