Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
type: Item
instance of: scholarly article
title: Convergence of the Lax-Friedrichs scheme and stability for conservation laws with a discontinuous space-time dependent flux
zbMATH Open document ID: 1112.65085
DOI: 10.1142/S0252959904000299
published in: Chinese Annals of Mathematics. Series B
publication date: 2005-03-07T00:00:00Z
review text: The paper presents a convergence proof for the Lax-Friedrichs finite difference scheme in the context of non-convex genuinely nonlinear scalar conservation laws of the form \[ u_t+ f(k(x, t),u)_x= 0, \] where the coefficient \(k(x, t)\) is allowed to be discontinuous along curves in the \((x, t)\) plane. It is shown that a convergent subsequence of approximations produced by the Lax-Friedrichs scheme converges to an entropy solution, implying that the entire computed sequence converges.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 2141312
zbMATH Keywords: conservation laws
zbMATH Keywords: Lax-Friedrichs scheme
zbMATH Keywords: entropy condition
zbMATH Keywords: compensated compactness
zbMATH Keywords: nonconvex fluxes
author: Kenneth H. Karlsen
author: John D. Towers
MaRDI profile type: Publication
full work available at URL: s0252959904000299
OpenAlex ID: W2099854605
description: scientific article; zbMATH DE number 2141312