Geodesic
On monotonicity of CABARET scheme approximating the multidimensional scalar conservation law
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 4, pp. 431-440

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The monotonicity of the two-layer with respect to time CABARET scheme approximating the multidimensional scalar conservation law is analyzed. There is proposed a modification of this scheme. This modification of the CABARET scheme retains the monotonicity of the one-dimensional difference solutions in the linear approximation, and, as a result, it provides an increased smoothness during the calculation of the multidimensional discontinuous solutions. The results of test calculations are given. They illustrate the advantages of the modified scheme. 
@article{SJVM_2020_23_4_a5,
     author = {V. V. Ostapenko and T. V. Protopopova},
     title = {On monotonicity of {CABARET} scheme approximating the multidimensional scalar conservation law},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {431--440},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_4_a5/}
}
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V. V. Ostapenko; T. V. Protopopova. On monotonicity of CABARET scheme approximating the multidimensional scalar conservation law. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 4, pp. 431-440. http://geodesic.mathdoc.fr/item/SJVM_2020_23_4_a5/