# Boundary layer tails in periodic homogenization

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

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

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topAllaire, 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 -

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