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

Antoine Benoit 1, 2
2 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
Abstract : 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.
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Submitted on : Thursday, March 16, 2017 - 10:46:21 AM
Last modification on : Tuesday, October 9, 2018 - 10:37:33 AM
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Antoine Benoit. A necessary condition for the strong stability of finite difference scheme approximations for hyperbolic corner domains. 2017. ⟨hal-01490903⟩

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