Nonlinear stability of the relaxing schemes for scalar conservation laws
Tang, HZ
AbstractThe purpose of this paper is to study nonlinear stability of the relaxing schemes approximating nonconvex scalar conservation laws, constructed by Jin and Xin [4]. We will establish the maximum principle for a first-order and a second-order relaxing schemes presented in [4], if the initial layer is not introduced. Optimal bounds on the total variation and L-1-boundedness for the above schemes will also be obtained. Specifically, the conserved physical quantity in the relaxing schemes is TVD. The Lipschitz constant of the L-1 continuity in time is shown to be independent of the relaxation parameter epsilon and the time size k. These imply convergence of the above relaxing schemes. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
Keywordthe relaxing schemes maximum principle TVD hyperbolic conservation laws
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000170242800006
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Document Type期刊论文
Corresponding AuthorTang, HZ
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
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GB/T 7714
Tang, HZ. Nonlinear stability of the relaxing schemes for scalar conservation laws[J]. APPLIED NUMERICAL MATHEMATICS,2001,38(3):347-359.
APA Tang, HZ.(2001).Nonlinear stability of the relaxing schemes for scalar conservation laws.APPLIED NUMERICAL MATHEMATICS,38(3),347-359.
MLA Tang, HZ."Nonlinear stability of the relaxing schemes for scalar conservation laws".APPLIED NUMERICAL MATHEMATICS 38.3(2001):347-359.
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