A necessary condition for the strong stability of finite difference scheme approximations for hyperbolic corner domains

Antoine Benoit (1, 2)

1 ULB - Université libre de Bruxelles
2 MEPHYSTO - Quantitative methods for stochastic models in physics

This article study the strong stability of finite difference scheme approximations for hyperbolic systems of equations in the quarter space. The main result is that as in the continuous framework of PDE impose the so-called uniform GKS condition (which is the condition characterizing the strong stability of the finite difference scheme approximations in the half space) on each side of the quarter space is not sufficient to ensure the strong stability of the scheme in the quarter space. We decribe in this paper a new necessary inversibility condition. This condition seems to be some discretized version of the condition imposed in [Osh73] in the PDE framework.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Antoine Benoit. A necessary condition for the strong stability of finite difference scheme approximations for hyperbolic corner domains. 2017. ⟨hal-01490903⟩