A MULTISCALE CORRECTION METHOD FOR LOCAL SINGULAR PERTURBATIONS OF THE BOUNDARY

Marc Dambrine (1) , Grégory Vial (2)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uε 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 uε based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results.

Mots clés: Multiscale asymptotic analysis; Shape optimization; Patch of elements

Domaines: Analyse numérique [math.NA]

Marc Dambrine, Grégory Vial. A MULTISCALE CORRECTION METHOD FOR LOCAL SINGULAR PERTURBATIONS OF THE BOUNDARY. ESAIM: Mathematical Modelling and Numerical Analysis, 2007, 41 (1), pp.111-127. ⟨10.1051/m2an:2007012⟩. ⟨hal-00085376⟩