A MULTISCALE CORRECTION METHOD FOR LOCAL SINGULAR PERTURBATIONS OF THE BOUNDARY

International audienceIn 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