| Issue |
ESAIM: M2AN
Volume 41, Number 1, January-February 2007
|
|
|---|---|---|
| Page(s) | 111 - 127 | |
| DOI | https://doi.org/10.1051/m2an:2007012 | |
| Published online | 26 April 2007 | |
A multiscale correction method for local singular perturbations of the boundary
1
LMAC, Université de Technologie de Compiègne, France.
2
IRMAR, Antenne de Bretagne de l'ENS Cachan, France. gvial@bretagne.ens-cachan.fr
Received:
12
June
2006
Revised:
8
November
2006
Revised:
15
November
2006
In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results.
Mathematics Subject Classification: 35B25 / 35B40 / 35J25 / 49Q10 / 65N30
Key words: Multiscale asymptotic analysis / shape optimization / patch of elements.
© EDP Sciences, SMAI, 2007
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