Instability of travelling wave profiles for the lax-friedrichs scheme

Paolo Baiti; Alberto Bressan; Helge Kristian Jenssen

doi:10.3934/dcds.2005.13.877

Instability of travelling wave profiles for the lax-friedrichs scheme

Paolo Baiti, Alberto Bressan, Helge Kristian Jenssen

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7 Scopus citations

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 λ_n → λ, the corresponding profiles Ψ_n converge to a limit Ψ uniformly on the real line, but Tot.Var.{Ψ_n - Ψ} ≥ c₀ > 0 for all n.

Original language	English (US)
Pages (from-to)	877-899
Number of pages	23
Journal	Discrete and Continuous Dynamical Systems
Volume	13
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2005.13.877
State	Published - Nov 2005

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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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.",

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AU - Bressan, Alberto

AU - Jenssen, Helge Kristian

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N2 - 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.

AB - 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.

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IS - 4

ER -

Instability of travelling wave profiles for the lax-friedrichs scheme

Abstract

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