Matching and multiscale expansions for a model singular perturbation problem
Sébastien Tordeux, Grégory Vial, Monique Dauge · Comptes Rendus Mathématique · 2006
We consider the Laplace–Dirichlet equation in a polygonal domain which is perturbed at the scale ε near one of its vertices. We assume that this perturbation is self-similar, that is, derives from the same pattern for all values of ε . On the base of this model problem, we compare two different approaches: the method of matched asymptotic expansions and the method of multiscale expansion. We enlighten the specificities of both techniques, and show how to switch from one expansion to the other.