Instability of travelling wave profiles for the lax-friedrichs scheme

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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.

Original languageEnglish (US)
Pages (from-to)877-899
Number of pages23
JournalDiscrete and Continuous Dynamical Systems
Volume13
Issue number4
DOIs
StatePublished - Nov 2005

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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