Instability of travelling wave profiles for the Lax-Friedrichs scheme (Q2574733)

The authors considered travelling wave profiles for discrete approximations to hyperbolic system of conservation laws. A detailed example is constructed, showing that the Lax-Friedrichs scheme the travelling profiles do not dependent continuously on the wave speed, in the BV norm. Namely, taking a sequence of wave speeds \(\lambda_n \to \lambda\), the corresponding profiles \(\psi_n\) converge to a limit \(\psi\) uniformly on the real line, but Tot. Var\( \{\psi n -\psi\}\geq c_0 > 0\) for all \(n\).