A multiscale correction method for local singular perturbations of the boundary

Dambrine, Marc; Vial, Grégory

ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 111-127.

In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution $u_{\epsilon }$ of a second order elliptic equation posed in the perturbed domain with respect to the size parameter $\epsilon$ of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of $u_{\epsilon }$ based on a multiscale superposition of the unperturbed solution $u_0$ and a profile defined in a model domain. We conclude with numerical results.

Classification : 35B25, 35B40, 35J25, 49Q10, 65N30
Mots clés : multiscale asymptotic analysis, shape optimization, patch of elements

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