Le regain d'intérêt pour la théorie de la supraconductivté motive les travaux liés à la détermination de l'état fondamental de l'opérateur de Schrödinger avec champ magnétique. Dans cet article, nous proposons une approche numérique basée sur la méthode des éléments finis afin de déterminer le bas du spectre de cet opérateur dans des domaines généraux. Nous améliorons les résultats numériques à l'aide de techniques de raffinement de maillages liées aux estimateurs a posteriori développés ailleurs. Nous regardons également la monotonie du bas du spectre sur un secteur angulaire selon l'angle du domaine afin de compléter l'étude théorique de Bonnaillie (C. R. Acad. Sci. Paris, Ser. I 336 (2) (2003) 135–140).
Motivated by the superconductivity, we are interested in the fundamental state of the Schorödinger operator with magnetic field. In this paper, we propose a numerical approach based on the finite elements method to determine the bottom of the spectrum of this operator in general domains. We improve the numerical results by using mesh-refinement techniques based on a posteriori error estimators developed elsewhere. We also look at the monotonicity of the bottom of the spectrum in an angular sector according to the angle to complement the theorical study of Bonnaillie (C. R. Acad. Sci. Paris, Ser. I 336 (2) (2003) 135–140).
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@article{CRMATH_2003__337_8_543_0,
author = {Fran\c{c}ois Alouges and Virginie Bonnaillie},
title = {Analyse num\'erique de la supraconductivit\'e},
journal = {Comptes Rendus. Math\'ematique},
pages = {543--548},
publisher = {Elsevier},
volume = {337},
number = {8},
year = {2003},
doi = {10.1016/j.crma.2003.09.007},
language = {fr},
}
François Alouges; Virginie Bonnaillie. Analyse numérique de la supraconductivité. Comptes Rendus. Mathématique, Volume 337 (2003) no. 8, pp. 543-548. doi : 10.1016/j.crma.2003.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.007/
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On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners
Virginie Bonnaillie
C. R. Math (2003)