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

Huazhong Tang;  Gerald Warnecke — 2004

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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 ( 2 K + 1 ) -point monotone scheme may give an oscillatory solution even though...

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

Huazhong Tang;  Gerald Warnecke — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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. This note will investigate this problem from a numerical point of view and show that a -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.

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