no. 17-18
Numerical analysis
L2 stability of nonlinear finite-volume schemes for linear hyperbolic systems
[Stabilité L2 des schémas volumes finis non linéaires pour les systèmes hyperboliques linéaires]

Présenté par : Philippe G. Ciarlet

Ndjinga, Michaël1
1 CEA-Saclay, DEN, DM2S, STMF, LMEC, F-91191 Gif-sur-Yvette, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 707-711.

Dans cette Note, nous démontrons la stabilité L2 dʼune grande classe de schémas volumes finis pour la résolution des systèmes hyperboliques dʼéquations aux dérivées partielles linéaires sur maillages non structurés. Cette classe inclut des schémas non linéaires, qui peuvent être sous forme explicite ou implicite. On donne également une borne sur le conditionnement de la version implicite des schémas.

In this Note we prove the L2 stability of a large class of finite-volume schemes applied to hyperbolic systems of linear partial differential equations on multidimensional unstructured meshes. This class includes nonlinear schemes that could be either explicit or implicit. We also derive a bound on the condition number of the implicit version of the schemes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.008
Ndjinga, Michaël 1

1 CEA-Saclay, DEN, DM2S, STMF, LMEC, F-91191 Gif-sur-Yvette, France 
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Ndjinga, Michaël. $ {L}^{2}$ stability of nonlinear finite-volume schemes for linear hyperbolic systems. Comptes Rendus. Mathématique, Tome 351 (2013) no. 17-18, pp. 707-711. doi : 10.1016/j.crma.2013.09.008. http://www.numdam.org/articles/10.1016/j.crma.2013.09.008/

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