A note on (2𝖪+1)-point conservative monotone schemes
Tang, Huazhong ; Warnecke, Gerald
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004), p. 345-357 / Harvested from Numdam
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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.

Publié le : 2004-01-01
DOI : https://doi.org/10.1051/m2an:2004016
Classification:  35L65,  65M06,  65M10 
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     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},
     volume = {38},
     year = {2004},
     pages = {345-357},
     doi = {10.1051/m2an:2004016},
     mrnumber = {2069150},
     zbl = {1075.65113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2004__38_2_345_0}
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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, Tome 38 (2004) pp. 345-357. doi : 10.1051/m2an:2004016. http://gdmltest.u-ga.fr/item/M2AN_2004__38_2_345_0/

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