A multiscale correction method for local singular perturbations of the boundary
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 1, p. 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.

DOI : https://doi.org/10.1051/m2an:2007012
Classification:  35B25,  35B40,  35J25,  49Q10,  65N30
Keywords: multiscale asymptotic analysis, shape optimization, patch of elements
@article{M2AN_2007__41_1_111_0,
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},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
pages = {111-127},
doi = {10.1051/m2an:2007012},
zbl = {1129.65084},
mrnumber = {2323693},
language = {en},
url = {http://www.numdam.org/item/M2AN_2007__41_1_111_0}
}

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, Volume 41 (2007) no. 1, pp. 111-127. doi : 10.1051/m2an:2007012. http://www.numdam.org/item/M2AN_2007__41_1_111_0/

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