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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 good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a (2K+1)-point monotone scheme may give an oscillatory solution even though the approximate solution is total variation diminishing, and satisfies maximum principle as well as discrete entropy inequality.

Keywords

Hyperbolic conservation lawsfinite difference schememonotone schemeconvergenceoscillation.
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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