A note on (2𝖪+1)-point conservative monotone schemes
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 345-357.

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.

DOI : 10.1051/m2an:2004016
Classification : 35L65, 65M06, 65M10
Mots clés : hyperbolic conservation laws, finite difference scheme, monotone scheme, convergence, oscillation
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     title = {A note on $\sf (2K+1)$-point conservative monotone schemes},
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Tang, Huazhong; Warnecke, Gerald. A note on $\sf (2K+1)$-point conservative monotone schemes. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 345-357. doi : 10.1051/m2an:2004016. http://www.numdam.org/articles/10.1051/m2an:2004016/

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