Sixth order weighted essentially non-oscillatory schemes with Z-type nonlinear weighting procedure for nonlinear degenerate parabolic equations

In this paper we develop new nonlinear weights of sixth order finite difference weighted essentially non-oscillatory (WENO) schemes for nonlinear degenerate parabolic equations. We construct two Z-type nonlinear weights: one is based on the $L^2$ norm and the other depends on the $L^1$ norm, yielding improved WENO schemes with more accurate resolution. We also confirm that the new devised nonlinear weights satisfy the sufficient conditions of sixth order accuracy. Finally, one- and two-dimensional numerical examples are presented to demonstrate the improved behavior of WENO schemes with new weighting procedure.