A multiscale correction method for local singular perturbations of the boundary
ESAIM: Mathematical Modelling and Numerical Analysis - 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 : https://doi.org/10.1051/m2an:2007012
Classification : 35B25,  35B40,  35J25,  49Q10,  65N30
Mots clés : multiscale asymptotic analysis, shape optimization, patch of elements
     author = {Dambrine, Marc and Vial, Gr\'egory},
     title = {A multiscale correction method for local singular perturbations of the boundary},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {111--127},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/m2an:2007012},
     zbl = {1129.65084},
     mrnumber = {2323693},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an:2007012/}
Dambrine, Marc; Vial, Grégory. A multiscale correction method for local singular perturbations of the boundary. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 1, pp. 111-127. doi : 10.1051/m2an:2007012. http://archive.numdam.org/articles/10.1051/m2an:2007012/

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