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| 具有对数势能的Cahn-Hilliard方程的有限元算法 | |
| 引用本文： | 王星星 王旦霞. 具有对数势能的Cahn-Hilliard方程的有限元算法[J]. 应用数学, 2021, 34(2): 365-373 |
| 作者姓名： | 王星星 王旦霞 |
| 作者单位： | 太原理工大学数学学院, 山西 晋中 030600 |
| 基金项目： | 山西省重点研究开发项目(201903D121038);山西省自然科学基金项目(201901D111123)。 |
| 摘 要： | 本文我们提出了具有对数势能的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.运用正则性,将对数势能函数F(u)的定义域的范围由(-1,1)扩展到(-∞,∞).证明该方法是能量耗散的,并计算误差估计,最后通过数值算例对理论部分进行验证.结果表明,理论与数值算... |
| 关 键 词： | 对数势能 Cahn-Hilliard方程 混合有限元方法 误差估计 |
| 收稿时间： | 2020-04-19 |
Finite Element Method for the Cahn-Hilliard Equation with Logarithmic Potential |
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| WANG Xingxing,WANG Danxia. Finite Element Method for the Cahn-Hilliard Equation with Logarithmic Potential[J]. Mathematica Applicata, 2021, 34(2): 365-373 | |
| Authors: | WANG Xingxing WANG Danxia |
| Affiliation: | (College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China) |
| Abstract: | In this paper, we present a numerical scheme for the Cahn-Hilliard equation with logarithmic potential. In the space, the mixed finite element method is adopted for discrete, and the CrankNicolson scheme is adopted in the time. For the logarithmic potential, we use the regularization procedure,which make the domain for regularized function F(u) is extended from(-1, 1) to(-∞, ∞). Then we prove that the method is energy dissipative and calculate the error estimates. The verification and validation of the proposed method is conducted via numerical examples in the end. |
| Keywords: | Logarithmic potential Cahn-Hilliard equation Mixed finite element method Error estimate |
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