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Matching and multiscale expansions for a model singular perturbation problem. (English) Zbl 1109.35013
Summary: We consider the Laplace-Dirichlet equation in a polygonal domain which is perturbed at the scale \(\varepsilon\) near one of its vertices. We assume that this perturbation is self-similar, that is, derives from the same pattern for all values of \(\varepsilon\) . 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.

MSC:
35B25 Singular perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
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