Abstract In this paper, we consider the two-grid method for solving Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. This two-grid method consists of two steps. First step, solve the Cahn–Hilliard equation with full implicit mixed finite element method and Newton iteration method on a coarse grid. Second step, solve two linear equations on a fine grid. The stability and convergence of the proposed scheme are established. Finally, some numerical experiments are presented.

中文翻译：

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具有浓度依赖迁移率和对数 Flory-Huggins 体势的 Cahn-Hilliard 方程的有效双网格方法

摘要 在本文中，我们考虑求解具有浓度依赖迁移率和对数 Flory-Huggins 体势的 Cahn-Hilliard 方程的双网格方法。这种双网格方法包括两个步骤。第一步，在粗网格上用全隐式混合有限元法和牛顿迭代法求解 Cahn-Hilliard 方程。第二步，在细网格上求解两个线性方程。建立了所提出方案的稳定性和收敛性。最后，给出了一些数值实验。