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Article Dans Une Revue Comptes rendus de l'Académie des sciences. Série I, Mathématique Année : 2009

Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size

Résumé

This note presents the derivation of the second-order asymptotic expansion of the eigenvalues and the eigenfunctions of the operator associated to an interior elliptic equation supplemented by a Dirichlet boundary condition on a domain consisting of two cavities linked by a hole of small size. The asymptotic expansion is carried out with respect to the size of the hole. The main feature of the method is to yield a robust numerical procedure making it possible to compute the eigenvalues without resorting to a refined mesh around the hole.

Dates et versions

inria-00527437 , version 1 (19-10-2010)

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Abderrahmane Bendali, Alain Huard, Abdelkader Tizaoui, Sébastien Tordeux, Jean-Paul Vila. Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347 (19-20), pp.1147--1152. ⟨10.1016/j.crma.2009.09.005⟩. ⟨inria-00527437⟩
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