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

摘要

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 l~2-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 in Turkel (16(2): 109-129, 1977).