The use of smoothing operators in difference schemes of a high order of accuracy

On the strong monotonicity of the CABARET scheme

“…This is explained by the fact that the accuracy near the local extrema of the exact solution is reduced to the first order due to correction (1.6)-(1.8) of flux variables (1.5) used in the CABARET scheme. This shortcoming is inherent in many other higher order accurate schemes in which monotonicity [13][14][15] (or the TVD property [12,16]) is achieved via the minimax correction of the flux variables. A modified TVD scheme with the ENO property was proposed in [17] in order to overcome this shortcoming.…”