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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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##### References:
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