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A note on (2K+1)-point conservative monotone schemes

Published online by Cambridge University Press:  15 March 2004

Huazhong Tang  and
Gerald Warnecke
Huazhong Tang
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China, hztang@math.pku.edu.cn.
Gerald Warnecke
Affiliation:
Institüt für Analysis und Numerik, Otto–von–Guericke Universität Magdeburg, 39106 Magdeburg, Germany, Gerald.Warnecke@mathematik.uni-magdeburg.de.
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Abstract

First–order accurate monotone conservative schemes have goodconvergence and stability properties, and thus play a veryimportant role in designing modern high resolution shock-capturingschemes.Do the monotone difference approximations alwaysgive a good numerical solution in sense of monotonicity preservationor suppression of oscillations? This note will investigate this problemfrom a numerical point of view and show thata (2K+1)-point monotone scheme may give an oscillatory solutioneven though the approximate solution is total variation diminishing, andsatisfies maximum principle as well as discrete entropy inequality.

Keywords

Hyperbolic conservation lawsfinite difference schememonotone schemeconvergenceoscillation.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 345 - 357
Copyright
© EDP Sciences, SMAI, 2004

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