具有浓度迁移率和对数势能的修正Cahn-Hillard方程的有限元算法
Finite Element Method for the Modified Cahn-Hilliard Equation with the Concentration Mobility and the Logarithmic Potential
摘要: 为了研究具有浓度迁移率和对数势能的修正Cahn-Hilliard方程，在空间上采用混合有限元方法进行离散，时间上采用Crank-Nicolson格式进行离散，对于非线性项采用了凸分裂的方法。证明了数值方法的稳定性，并且给出了误差估计。最后，通过数值算例对理论分析进行了验证。结果表明，理论分析与数值实验相一致。
Abstract: In order to study the modified Cahn-Hilliard equation with concentration mobility and logarithmic potential energy, the mixed finite element method was used in space, and the Crank-Nicolson scheme was used in time. The convex splitting method is used for nonlinear terms. Furthermore, the stability of the numerical method is proved and the error estimate is given. Finally, a numerical example is given to verify the theoretical analysis. The results show that the theoretical analysis is consistent with the numerical experiment.
文章引用：李亚楠, 王旦霞, 任永华. 具有浓度迁移率和对数势能的修正Cahn-Hillard方程的有限元算法[J]. 应用数学进展, 2020, 9(9): 1383-1393. https://doi.org/10.12677/AAM.2020.99164

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