On the strong stability of finite difference schemes for hyperbolic systems in two space dimensions

Jean-François Coulombel (1)

1 Equations aux dérivées partielles

We study the stability of some finite difference schemes for symmetric hyperbolic systems in two space dimensions. For the so-called upwind scheme and the Lax-Wendroff scheme with a stabilizer, we show that stability is equivalent to strong stability, meaning that both schemes are either unstable or L2-decreasing. These results improve on a series of partial results on strong stability. We also show that, for the Lax-Wendroff scheme without stabilizer, strong stability may not occur no matter how small the CFL parameters are chosen. This partially invalidates some of Turkel's conjectures.

Mots clés: Hyperbolic systems; finite difference schemes; stability

Domaines: Analyse numérique [math.NA]

Jean-François Coulombel. On the strong stability of finite difference schemes for hyperbolic systems in two space dimensions. Calcolo, 2014, 51 (1), pp.97-108. ⟨hal-00727417⟩