A multiscale correction method for local singular perturbations of the boundary
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 ε 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 u ε based on a multiscale superposition of the unperturbed solution u 0 and a profile defined in a model domain. We conclude with numerical results.

DOI : 10.1051/m2an:2007012
Classification : 35B25, 35B40, 35J25, 49Q10, 65N30
Mots clés : multiscale asymptotic analysis, shape optimization, patch of elements
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Dambrine, Marc; Vial, Grégory. A multiscale correction method for local singular perturbations of the boundary. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 111-127. doi : 10.1051/m2an:2007012. http://www.numdam.org/articles/10.1051/m2an:2007012/

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