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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
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume134Issue:1-2Pages:343-367
AbstractThis 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.
KeywordRuijgrok-Wu model splitting scheme convergence stability
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000170719000022
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/16271
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ Magdeburg, IAN, D-39016 Magdeburg, Germany
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100864, Peoples R China
Recommended Citation
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.
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