Nous nous intéressons aux inégalités discrètes d'entropie pour une classe de schémas de relaxation. Après une brève description de la méthode, nous proposons une démonstration directe pour établir les inégalités discrètes d'entropie. Ces inégalités sont, en fait, la conséquence d'un principe de minimisation de l'entropie satisfait par le modèle de relaxation considéré. Ces résultats sont ensuite étendus au modèle aux 10 moments.
This work is devoted to the discrete entropy inequalities when considering relaxation schemes. After describing the numerical method, we propose a direct proof to establish the discrete entropy inequalities. In fact, we show that the considered relaxation model satisfies a minimum principle on the entropy. This principle implies the expected inequalities. The work is concluded when applying the above results to the 10 moment model.
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@article{CRMATH_2005__340_1_63_0,
author = {Berthon, Christophe},
title = {In\'egalit\'es d'entropie pour un sch\'ema de relaxation},
journal = {Comptes Rendus. Math\'ematique},
pages = {63--68},
publisher = {Elsevier},
volume = {340},
number = {1},
year = {2005},
doi = {10.1016/j.crma.2004.10.008},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.10.008/}
}
TY - JOUR AU - Berthon, Christophe TI - Inégalités d'entropie pour un schéma de relaxation JO - Comptes Rendus. Mathématique PY - 2005 SP - 63 EP - 68 VL - 340 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.10.008/ DO - 10.1016/j.crma.2004.10.008 LA - fr ID - CRMATH_2005__340_1_63_0 ER -
Berthon, Christophe. Inégalités d'entropie pour un schéma de relaxation. Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 63-68. doi : 10.1016/j.crma.2004.10.008. http://www.numdam.org/articles/10.1016/j.crma.2004.10.008/
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