Boundary layer tails in periodic homogenization

Grégoire Allaire; Micol Amar

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 4, page 209-243
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Allaire, Grégoire, and Amar, Micol. "Boundary layer tails in periodic homogenization ." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 209-243. <http://eudml.org/doc/197276>.

@article{Allaire2010,
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. },
author = {Allaire, Grégoire, Amar, Micol},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Boundary layers; periodic functions; asymptotic expansion; homogenization.; rectangular domains having either fixed or oscillating boundary; homogenized equation; effective Fourier boundary conditions},
language = {eng},
month = {3},
pages = {209-243},
publisher = {EDP Sciences},
title = {Boundary layer tails in periodic homogenization },
url = {http://eudml.org/doc/197276},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Allaire, Grégoire
AU - Amar, Micol
TI - Boundary layer tails in periodic homogenization
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 209
EP - 243
AB - 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.
LA - eng
KW - Boundary layers; periodic functions; asymptotic expansion; homogenization.; rectangular domains having either fixed or oscillating boundary; homogenized equation; effective Fourier boundary conditions
UR - http://eudml.org/doc/197276
ER -

References

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