Volume 41, Number 1, January-February 2007
|Page(s)||111 - 127|
|Published online||26 April 2007|
A multiscale correction method for local singular perturbations of the boundary
LMAC, Université de Technologie de Compiègne, France.
2 IRMAR, Antenne de Bretagne de l'ENS Cachan, France. email@example.com
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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