Numerical Analysis
Spectral stability of finite volume schemes for linear hyperbolic systems
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1111-1115.

In this Note we prove the spectral stability of a large class of finite volume schemes applied to hyperbolic systems of linear partial differential equations on multidimensional unstructured meshes. This class requires that the upwinding matrix has positive eigenvalues and is codiagonalisable with the system matrices. That includes among others the upwind and centred implicit schemes, and the upwind explicit scheme under a CFL condition.

Dans cette Note nous démontrons la stabilité spectrale dʼune grande classe de schémas volumes finis pour la résolution des systèmes hyperboliques dʼéquations aux dérivées partielles linéaires sur maillages non structurés. Cette classe requiert que la matrice de décentrement ait des valeurs propres positives et soit codiagonalisable avec les matrices du système. Elle inclut notament les schémas centré et décentré amont implicites, et le schéma décentré amont explicite sous une condition CFL.

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DOI: 10.1016/j.crma.2011.09.011
Ndjinga, Michaël 1

1 Commissariat à lʼénergie atomique, centre de Saclay, DEN, DM2S, SFME, 91191 Gif-sur-Yvette, France
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Ndjinga, Michaël. Spectral stability of finite volume schemes for linear hyperbolic systems. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1111-1115. doi : 10.1016/j.crma.2011.09.011. http://www.numdam.org/articles/10.1016/j.crma.2011.09.011/

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