Comptes Rendus
no. 17-18
Numerical analysis
L2 stability of nonlinear finite-volume schemes for linear hyperbolic systems

Presented by: Philippe G. Ciarlet

Michaël Ndjinga1
1 CEA-Saclay, DEN, DM2S, STMF, LMEC, F-91191 Gif-sur-Yvette, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 707-711.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.09.008

Michaël Ndjinga 1

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

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