[Développements raccordé et multi-échelle pour un problème de perturbation singulière modèle]
On considère le problème de Laplace–Dirichlet dans un domaine polygonal qui présente une perturbation de taille ε en l'un de ses sommets. Cette perturbation est supposée auto-similaire, i.e. provient d'un motif fixe dilaté à l'échelle ε. Sur ce problème modèle, nous mettons en œuvre deux méthodes : développements asymptotiques raccordés et développement multi-échelle. Nous mettons en évidence les particularités de chaque approche et montrons comment passer d'un développement à l'autre.
We consider the Laplace–Dirichlet equation in a polygonal domain which is perturbed at the scale ε near one of its vertices. We assume that this perturbation is self-similar, that is, derives from the same pattern for all values of ε. On the base of this model problem, we compare two different approaches: the method of matched asymptotic expansions and the method of multiscale expansion. We enlighten the specificities of both techniques, and show how to switch from one expansion to the other.
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@article{CRMATH_2006__343_10_637_0,
author = {Tordeux, S\'ebastien and Vial, Gr\'egory and Dauge, Monique},
title = {Matching and multiscale expansions for a model singular perturbation problem},
journal = {Comptes Rendus. Math\'ematique},
pages = {637--642},
publisher = {Elsevier},
volume = {343},
number = {10},
year = {2006},
doi = {10.1016/j.crma.2006.10.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.10.010/}
}
TY - JOUR AU - Tordeux, Sébastien AU - Vial, Grégory AU - Dauge, Monique TI - Matching and multiscale expansions for a model singular perturbation problem JO - Comptes Rendus. Mathématique PY - 2006 SP - 637 EP - 642 VL - 343 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.10.010/ DO - 10.1016/j.crma.2006.10.010 LA - en ID - CRMATH_2006__343_10_637_0 ER -
%0 Journal Article %A Tordeux, Sébastien %A Vial, Grégory %A Dauge, Monique %T Matching and multiscale expansions for a model singular perturbation problem %J Comptes Rendus. Mathématique %D 2006 %P 637-642 %V 343 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.10.010/ %R 10.1016/j.crma.2006.10.010 %G en %F CRMATH_2006__343_10_637_0
Tordeux, Sébastien; Vial, Grégory; Dauge, Monique. Matching and multiscale expansions for a model singular perturbation problem. Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 637-642. doi : 10.1016/j.crma.2006.10.010. http://www.numdam.org/articles/10.1016/j.crma.2006.10.010/
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