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Kruzkov's estimates for scalar conservation laws revisited

Author(s): F. Bouchut; B. Perthame
Journal: Trans. Amer. Math. Soc. 350 (1998), 2847-2870.
MSC (1991): Primary 65M15, 35L65, 35B30.
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Abstract: We give a synthetic statement of Kruzkov-type estimates for multi-dimensional scalar conservation laws. We apply it to obtain various estimates for different approximation problems. In particular we recover for a model equation the rate of convergence in $h^{1/4}$ known for finite volume methods on unstructured grids.

Les estimations de Kruzkov pour les lois de conservation scalaires revisitées

Résumé Nous donnons un énoncé synthétique des estimations de type de Kruzkov pour les lois de conservation scalaires multidimensionnelles. Nous l'appliquons pour obtenir d'estimations nombreuses pour problèmes différents d'approximation. En particulier, nous retrouvons pour une équation modèle la vitesse de convergence en $h^{1/4}$ connue pour les méthodes de volumes finis sur des maillages non structurés.

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Additional Information:

F. Bouchut
Affiliation: Université d'Orléans et CNRS, UMR 6628, Dépt. de Mathématiques, BP 6759, 45067 Orléans cedex 2, France
Email: fbouchut@labomath.univ-orleans.fr

B. Perthame
Affiliation: Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique et URA 189, BC 187, 4 place Jussieu, 75252 Paris cedex 05, France
Email: perthame@ann.jussieu.fr

DOI: 10.1090/S0002-9947-98-02204-1
PII: S 0002-9947(98)02204-1
Keywords: Multi-dimensional scalar conservation laws, error estimates, entropy inequalities, finite volumes. \indent\textit{Mots-cl\'es}. Lois de conservation scalaires multidimensionnelles, estimations d'erreur, in\'egalit\'es d'entropie, volumes finis
Received by editor(s): July 8, 1996
Copyright of article: Copyright 1998, American Mathematical Society

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The following works have cited this article

Eymard, R.; Gallouët, T.; Ghilani, M.; Herbin, R., Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes, IMA J. Numer. Anal. 18 (1998), 563--594. (English)

Katsoulakis, M. A.; Kossioris, G.; Makridakis, Ch., Convergence and error estimates of relaxation schemes for multidimensional conservation laws, Comm. Partial Differential Equations 24 (1999), 395--424. (English) MR CMP 1 683 045


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