Abstract: We study travelling wave profiles for discrete approximations to hyperbolic systems of conservation laws. A detailed example is constructed, showing that for the Lax–Friedrichs scheme the travelling profiles do not depend continuously on the wave speed, in the BV norm. Namely, taking a sequence of wave speeds λn→λ, the corresponding profiles Ψn converge to a limit Ψ uniformly on the real line, but Tot.Var.{Ψn-Ψ}≥c0>0 for all n.
Conservation Laws Preprint Server <conservation@math.ntnu.no> 2004-07-22 17:06:27 UTC