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

Published online by Cambridge University Press:  15 March 2004

Huazhong Tang
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China, [email protected].
Gerald Warnecke
Affiliation:
Institüt für Analysis und Numerik, Otto–von–Guericke Universität Magdeburg, 39106 Magdeburg, Germany, [email protected].
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2004

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