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Journal Articles Comptes Rendus. Mathématique Year : 2017

Eigenvalue problems with sign-changing coefficients

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Abstract

We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious modes. We also prove localisation results of the eigenfunctions for certain sets of coefficients.
Nous étudions, d’un point de vue théorique et numérique, des problèmes aux valeurs propres mettant en jeu des coefficients dont le signe change sur le domaine d’intérêt.
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Dates and versions

hal-01394856 , version 1 (10-11-2016)
hal-01394856 , version 2 (05-12-2017)

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Cite

Camille Carvalho, Lucas Chesnel, Patrick Ciarlet. Eigenvalue problems with sign-changing coefficients. Comptes Rendus. Mathématique, 2017, 355 (6), pp.671 - 675. ⟨10.1016/j.crma.2017.05.002⟩. ⟨hal-01394856v2⟩
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