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 -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.
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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {345--357},
year = {2004},
publisher = {EDP Sciences},
volume = {38},
number = {2},
doi = {10.1051/m2an:2004016},
mrnumber = {2069150},
zbl = {1075.65113},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2004016/}
}
TY - JOUR AU - Tang, Huazhong AU - Warnecke, Gerald TI - A note on $\sf (2K+1)$-point conservative monotone schemes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 345 EP - 357 VL - 38 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2004016/ DO - 10.1051/m2an:2004016 LA - en ID - M2AN_2004__38_2_345_0 ER -
%0 Journal Article %A Tang, Huazhong %A Warnecke, Gerald %T A note on $\sf (2K+1)$-point conservative monotone schemes %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 345-357 %V 38 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2004016/ %R 10.1051/m2an:2004016 %G en %F M2AN_2004__38_2_345_0
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
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