Stability conditions for the numerical solution of convection-dominated problems with skew-symmetric discretizations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.65155
DOI: 10.1137/100808472
published in: SIAM Journal on Numerical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.3313
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L02
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6070609
zbMATH Keywords: CFL condition
zbMATH Keywords: von Neumann stability
zbMATH Keywords: transport equation
zbMATH Keywords: Euler equation
zbMATH Keywords: Runge-Kutta schemes
zbMATH Keywords: Adams-Bashforth schemes
zbMATH Keywords: wave equation
author: Erwan Deriaz
MaRDI profile type: Publication
OpenAlex ID: W1980252718
arXiv ID: 1007.3313
title: Stability conditions for the numerical solution of convection-dominated problems with skew-symmetric discretizations
review text: The author presents the stability conditions for the numerical solution of convection-dominated problems with skew-symmetric discretizations. The paper is organized as follows. First the definition and the computation of the von Neumann stability are recalled. The linear transport problem, predicting a stability condition of the type \(\delta t \leq C(\delta x / u)^{2r / (2r - 1)}\) with \(r\) an integer, for several schemes are focused. Then the numerical schemes are constructed for which such a stability condition appears for \(r = 1,\,2,\,3,\,4\) and corresponds to exponents equal to \(2,\,\,\frac{4}{3},\,\,\frac{6}{5}\,\,\)and \(\frac{8}{7}\). Finally, it is shown how this stability criterion extends to nonlinear equations and to multicomponent transport equations (including wave equations).
reviewed by: Temur Jangveladze
description: scientific article; zbMATH DE number 6070609