[Problèmes aux valeurs propres en présence de coefficients changeant de signe]
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.
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.
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@article{CRMATH_2017__355_6_671_0,
author = {Carvalho, Camille and Chesnel, Lucas and Ciarlet, Patrick Jr.},
title = {Eigenvalue problems with sign-changing coefficients},
journal = {Comptes Rendus. Math\'ematique},
pages = {671--675},
publisher = {Elsevier},
volume = {355},
number = {6},
year = {2017},
doi = {10.1016/j.crma.2017.05.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.05.002/}
}
TY - JOUR AU - Carvalho, Camille AU - Chesnel, Lucas AU - Ciarlet, Patrick Jr. TI - Eigenvalue problems with sign-changing coefficients JO - Comptes Rendus. Mathématique PY - 2017 SP - 671 EP - 675 VL - 355 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.05.002/ DO - 10.1016/j.crma.2017.05.002 LA - en ID - CRMATH_2017__355_6_671_0 ER -
%0 Journal Article %A Carvalho, Camille %A Chesnel, Lucas %A Ciarlet, Patrick Jr. %T Eigenvalue problems with sign-changing coefficients %J Comptes Rendus. Mathématique %D 2017 %P 671-675 %V 355 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.05.002/ %R 10.1016/j.crma.2017.05.002 %G en %F CRMATH_2017__355_6_671_0
Carvalho, Camille; Chesnel, Lucas; Ciarlet, Patrick Jr. Eigenvalue problems with sign-changing coefficients. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 671-675. doi : 10.1016/j.crma.2017.05.002. http://www.numdam.org/articles/10.1016/j.crma.2017.05.002/
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