A note on (2𝖪+1)-point conservative monotone schemes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 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 : https://doi.org/10.1051/m2an:2004016
Classification:  35L65,  65M06,  65M10
Keywords: hyperbolic conservation laws, finite difference scheme, monotone scheme, convergence, oscillation
@article{M2AN_2004__38_2_345_0,
     author = {Tang, Huazhong and Warnecke, Gerald},
     title = {A note on $\sf (2K+1)$-point conservative monotone schemes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {2},
     year = {2004},
     pages = {345-357},
     doi = {10.1051/m2an:2004016},
     zbl = {1075.65113},
     mrnumber = {2069150},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_2_345_0}
}
Tang, Huazhong; Warnecke, Gerald. A note on $\sf (2K+1)$-point conservative monotone schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 345-357. doi : 10.1051/m2an:2004016. http://www.numdam.org/item/M2AN_2004__38_2_345_0/

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