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A multiscale correction method for local singular perturbations of the boundary

Published online by Cambridge University Press:  26 April 2007

Marc Dambrine and
Grégory Vial
Marc Dambrine
Affiliation:
LMAC, Université de Technologie de Compiègne, France.
Grégory Vial
Affiliation:
IRMAR, Antenne de Bretagne de l'ENS Cachan, France. gvial@bretagne.ens-cachan.fr
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Abstract

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 u 0 and a profile defined in a model domain. We conclude with numerical results.

Keywords

Multiscale asymptotic analysisshape optimizationpatch of elements.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 1 , January 2007, pp. 111 - 127
Copyright
© EDP Sciences, SMAI, 2007

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