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Journal of Computational Mathematics

Erratum to : “A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws”
Mehdi Badsi1; Christophe Berthon1; Ludovic Martaud1
1 Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 311-318.
corrects A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws

We, authors of the paper entitled “A family of second-order dissipative finite volume schemes for hyperbolic systems of conservations laws” present our apologies for many mistakes in the current version of the published paper. We explain below the mathematical mistakes and how to modify the assumption of the Theorem (4.2) to get the same conclusion (namely, the decay of the mass of the entropy). New material and a correct proof of the Theorem (4.2) are given. A corrected version of the published paper has been uploaded on HAL server at the adress: https://hal.science/hal-03564325.

Published online:
DOI: 10.5802/smai-jcm.103
Classification: 65N08, 35L65, 35L67
Keywords: Systems of conservation laws, Second-order finite Volume schemes, Explicit schemes, Global entropy inequality.
Mehdi Badsi 1; Christophe Berthon 1; Ludovic Martaud 1

1 Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Mehdi Badsi and Christophe Berthon and Ludovic Martaud},
     title = {Erratum to : {{\textquotedblleft}A} family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws{\textquotedblright}},
     journal = {The SMAI Journal of computational mathematics},
     pages = {311--318},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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     year = {2023},
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Mehdi Badsi; Christophe Berthon; Ludovic Martaud. Erratum to : “A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws”. The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 311-318. doi : 10.5802/smai-jcm.103. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.103/

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