[Stabilité spectrale des schémas volumes finis pour les systèmes hyperboliques linéaires]
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.
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.
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@article{CRMATH_2011__349_19-20_1111_0,
author = {Ndjinga, Micha\"el},
title = {Spectral stability of finite volume schemes for linear hyperbolic systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {1111--1115},
publisher = {Elsevier},
volume = {349},
number = {19-20},
year = {2011},
doi = {10.1016/j.crma.2011.09.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.09.011/}
}
TY - JOUR AU - Ndjinga, Michaël TI - Spectral stability of finite volume schemes for linear hyperbolic systems JO - Comptes Rendus. Mathématique PY - 2011 SP - 1111 EP - 1115 VL - 349 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.09.011/ DO - 10.1016/j.crma.2011.09.011 LA - en ID - CRMATH_2011__349_19-20_1111_0 ER -
%0 Journal Article %A Ndjinga, Michaël %T Spectral stability of finite volume schemes for linear hyperbolic systems %J Comptes Rendus. Mathématique %D 2011 %P 1111-1115 %V 349 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.09.011/ %R 10.1016/j.crma.2011.09.011 %G en %F CRMATH_2011__349_19-20_1111_0
Ndjinga, Michaël. Spectral stability of finite volume schemes for linear hyperbolic systems. Comptes Rendus. Mathématique, Tome 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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