Geodesic
A multiscale correction method for local singular perturbations of the boundary
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 111-127

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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.

DOI : 10.1051/m2an:2007012
Classification : 35B25, 35B40, 35J25, 49Q10, 65N30
Keywords: multiscale asymptotic analysis, shape optimization, patch of elements 
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     title = {A multiscale correction method for local singular perturbations of the boundary},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {111--127},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/m2an:2007012},
     mrnumber = {2323693},
     zbl = {1129.65084},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2007012/}
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Dambrine, Marc; Vial, Grégory. A multiscale correction method for local singular perturbations of the boundary. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 111-127. doi: 10.1051/m2an:2007012

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