In this paper, we propose a new finite difference weighted essentially non-oscillatory (WENO) scheme for nonlinear degenerate parabolic equations which may contain non-smooth solutions. An alternative formulation is designed to approximate the second derivatives in a conservative form. In this formulation, the odd order derivatives at half points are used to construct the numerical flux, instead of the usual practice of reconstruction. Moreover, the multi-resolution WENO scheme is designed to circumvent the negative ideal weights and mapped nonlinear weights that appear when applying the standard WENO idea. We will describe the scheme formulation and present numerical tests for one- and two-dimensional, demonstrating the designed high order accuracy and non-oscillatory performance of the schemes constructed in this paper.

在本文中，我们针对可能包含非光滑解的非线性退化抛物方程提出了一种新的有限差分加权基本非振荡（WENO）方案。设计一种替代的公式，以保守的形式近似二阶导数。在此公式中，半点的奇数阶导数用于构造数值通量，而不是通常的重建方法。此外，多分辨率WENO方案旨在避免应用标准WENO想法时出现的负理想权重和映射的非线性权重。我们将描述该方案的公式并针对一维和二维进行数值测试，以证明本文构建的方案的设计高阶精度和非振荡性能。