A multiscale correction method for local singular perturbations of the boundary
Dambrine, Marc ; Vial, Grégory
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007), p. 111-127 / Harvested from Numdam
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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.

Publié le : 2007-01-01
DOI : https://doi.org/10.1051/m2an:2007012
Classification:  35B25,  35B40,  35J25,  49Q10,  65N30 
@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},
     volume = {41},
     year = {2007},
     pages = {111-127},
     doi = {10.1051/m2an:2007012},
     mrnumber = {2323693},
     zbl = {1129.65084},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 41 (2007) pp. 111-127. doi : 10.1051/m2an:2007012. http://gdmltest.u-ga.fr/item/M2AN_2007__41_1_111_0/

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