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Jean-François Coulombel
The Leray-Gårding method for finite difference schemes
(La méthode de Leray et Gårding pour les schémas aux différences finies)
Journal de l'École polytechnique — Mathématiques, 2 (2015), p. 297-331, doi: 10.5802/jep.25
Article PDF | TeX source
Class. Math.: 65M06, 65M12, 35L03, 35L04
Mots clés: Équations hyperboliques, différences finies, stabilité, conditions aux limites, semi-groupe

Résumé - Abstract

Dans les années 1950, Leray et Gårding ont développé une technique de multiplicateur pour obtenir des estimations a priori de solutions d’équations hyperboliques scalaires. L’existence d’un multiplicateur est le point de départ du travail de Rauch [23] pour montrer des estimations de semi-groupe pour les problèmes aux limites hyperboliques. Dans cet article, nous expliquons comment cette technique de multiplicateur peut être adaptée au cadre des schémas aux différences finies pour les équations de transport. Ce travail s’applique à des schémas numériques multi-pas en temps. L’existence et les propriétés du multiplicateur nous permettent d’obtenir des estimations de semi-groupe optimales pour des versions totalement discrètes des problèmes aux limites hyperboliques.

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