Stability of finite difference schemes for hyperbolic initial boundary value problems

Jean-François Coulombel (1)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids

We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming stability for the dicretization of the hyperbolic operator as well as a geometric regularity condition, we show that an appropriate determinant condition, that is the analogue of the uniform Kreiss-Lopatinskii condition for the continuous problem, yields strong stability for the discretized initial boundary value problem. The analysis relies on a suitable discrete block structure condition and the construction of suitable symmetrizers. Our work extends the results of Gustafsson, Kreiss, Sundstrom to a wider class of finite difference schemes.

Mots clés: finite difference schemes; stability; symmetrizers; Hyperbolic systems; boundary conditions

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

Jean-François Coulombel. Stability of finite difference schemes for hyperbolic initial boundary value problems. SIAM Journal on Numerical Analysis, 2009, 47 (4), pp.2844-2871. ⟨hal-00339527v2⟩