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:通过使用两种不同的非以中心为中心的流动近似值,提出了两种新的数字方案,以接近卡恩-希利亚德等式的下降流动性(稳定值0和1之间),我们证明这两种方案都具有能源稳定性,并大致保留了最大原则,也就是说,在间距[0]之外,解决办法的数量从短距参数计算为零。此外,我们提出若干数字结果,以显示拟议方案的准确性和良好行为,同时将两种方案与相应的中心方案进行比较。