Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation

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	Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation
	Liu, HL ; Wang, JH ; Warnecke, G
	2001-09-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	134 期号:1-2 页码:343-367
摘要	This paper deals with upwind splitting schemes for the Ruijgrok-Wu model (Physica A 113 (1982) 401-416) of the kinetic theory of rarefied gases in the fluid-dynamic scaling. We prove the stability and the convergence for these schemes. The relaxation limit is also investigated and the limit equation is proved to be a first-order quasi-linear conservation law. The loss of quasi-monotonicity of the present model makes it necessary to give a more careful analysis of its structure. We also obtain global error estimates in the spaces Ws-p for -1 less than or equal to s less than or equal to 1/p, 1 less than or equal to p less than or equal to infinity and pointwise error estimates for the approximate solution. The proof naturally uses the framework introduced by Nessyahu and Tadmor (SIAM J. Numer Anal. 29 (1992) 1505-1519) due to the convexity of the flux function. (C) 2001 Elsevier Science B.V. All rights reserved.
关键词	Ruijgrok-Wu model splitting scheme convergence stability
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000170719000022
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16271
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, HL
作者单位	1.Univ Magdeburg, IAN, D-39016 Magdeburg, Germany 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100864, Peoples R China
推荐引用方式 GB/T 7714	Liu, HL,Wang, JH,Warnecke, G. Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2001,134(1-2):343-367.
APA	Liu, HL,Wang, JH,&Warnecke, G.(2001).Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,134(1-2),343-367.
MLA	Liu, HL,et al."Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 134.1-2(2001):343-367.