Geodesic
Modification of the Cabaret scheme ensuring its high accuracy on local extrema
Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 21-31

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It's shown that the standard flux correction which is necessary for monotonicity of the CABARET scheme leads to reduction of its accuracy near local extrema. Modified flux correction is proposed that ensures the strong monotonicity of the CABARET scheme for Courant numbers $r\in (0,0.5]$ and simultaneously preserves its high accuracy near local extrema. Test computations of discontinuous solutions of nonlinear advection equation are presented that illustrate advantages of modified scheme.
Keywords: CABARET finite difference scheme, strong monotonicity, flux corrected transport. 
@article{MM_2015_27_10_a2,
     author = {N. A. Zyuzina and V. V. Ostapenko},
     title = {Modification of the {Cabaret} scheme ensuring its high accuracy on local extrema},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {21--31},
     publisher = {mathdoc},
     volume = {27},
     number = {10},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_10_a2/}
}
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N. A. Zyuzina; V. V. Ostapenko. Modification of the Cabaret scheme ensuring its high accuracy on local extrema. Matematičeskoe modelirovanie, Tome 27 (2015) no. 10, pp. 21-31. http://geodesic.mathdoc.fr/item/MM_2015_27_10_a2/