Two new numerical schemes to approximate the Cahn-Hilliard equation with degenerate mobility (between stable values 0 and 1) are presented, by using two different non-centered approximation of the mobility. We prove that both schemes are energy stable and preserve the maximum principle approximately, i.e. the amount of the solution being outside of the interval [0,1] goes to zero in terms of a truncation parameter. Additionally, we present several numerical results in order to show the accuracy and the well behavior of the proposed schemes, comparing both schemes and the corresponding centered scheme.

翻译：给出了两种采用非中心迁移率逼近方法的数值格式，用于近似求解退化迁移率（稳定值介于0和1之间）的Cahn-Hilliard方程。我们证明了两种格式均为能量稳定的，并能近似保持最大值原理，即解在区间[0,1]之外的部分随截断参数趋近于零。此外，我们通过多个数值结果展示了所提格式的精度和良好行为，并对两种格式与相应的中心格式进行了比较。