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Boundary layer tails in periodic homogenization

Published online by Cambridge University Press:  15 August 2002

Grégoire Allaire  and
Micol Amar
Grégoire Allaire
Affiliation:
Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, Paris VI, Tour 55–65, 4 place Jussieu, 70005 Paris, France; [email protected].
Micol Amar
Affiliation:
Dipartimento Me.Mo.Mat, Università “La Sapienza" - Roma, Via A. Scarpa 16, 00161 Roma, Italy; [email protected].
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Abstract

This paper focus on the properties of boundary layers in periodic homogenization in rectangular domains which are either fixed or have an oscillating boundary. Such boundary layers are highly oscillating near the boundary and decay exponentially fast in the interior to a non-zero limit that we call boundary layer tail. The influence of these boundary layer tails on interior error estimates is emphasized. They mainly have two effects (at first order with respect to the period ε): first, they add a dispersive term to the homogenized equation, and second, they yield an effective Fourier boundary condition.

Keywords

Boundary layersperiodic functionsasymptotic expansionhomogenization.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 209 - 243
Copyright
© EDP Sciences, SMAI, 1999

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