On the convergence of numerical schemes for the Boltzmann equation.
type: Item
instance of: scholarly article
title: On the convergence of numerical schemes for the Boltzmann equation.
zbMATH Open document ID: 1038.82082
DOI: 10.1016/S0294-1449(02)00029-X
author: D. Massart
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2003-09-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78595
review text: The aim of the paper is to consider explicit discretization schemes in time and space for the Boltzman equations. Thereby, Maxwellian bounds on the resulting approximated solution are proven and the convergence is derived by means of a new time-discrete averaging lemma.
Mathematics Subject Classification ID: 82C80
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1975932
zbMATH Keywords: explicit discretization schemes
zbMATH Keywords: Maxwellian bounds
zbMATH Keywords: time-discrete averaging lemma
MaRDI profile type: Publication
cites work: Q3733269
cites work: Averaging lemmas without time Fourier transform and application to discretized kinetic equations
cites work: The Boltzmann equation and its applications
cites work: ABOUT THE SPLITTING ALGORITHM FOR BOLTZMANN AND B.G.K. EQUATIONS
cites work: On the Cauchy problem for Boltzmann equations: Global existence and weak stability
cites work: Global weak solutions of Vlasov‐Maxwell systems
cites work: Global solutions of Boltzmann's equation and the entropy inequality
cites work: \(L^ p\) regularity of velocity averages
cites work: Relaxation Schemes for Nonlinear Kinetic Equations
cites work: Regularity of the moments of the solution of a transport equation
cites work: Q3719250
cites work: Q4838283
cites work: Régularité optimale des moyennes en vitesses, II
cites work: Q4001131
cites work: Approximation simultanée de réels par des nombres rationnels et noyau de collision de l'équation de Boltzmann
cites work: Convergence of discrete-velocity schemes for the Boltzmann equation
cites work: On the spatially homogeneous Boltzmann equation
cites work: Existence, stability, and convergence of solutions of discrete velocity models to the Boltzmann equation
cites work: A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation
cites work: A new consistent discrete-velocity model for the Boltzmann equation
cites work: A limiting case for velocity averaging
cites work: Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with \gamma=3
cites work: Time regularity for the system of isentropic gas dynamics with γ= 3
OpenAlex ID: W2046887112
description: scientific article; zbMATH DE number 1975932