具有对数势能的粘性Allen-Cahn方程的有限元算法  

Finite Element Method for Viscous Allen-Cahn Equation with Logarithmic Flory-Huggins Potential

作　　者：王云霞 王旦霞 贾宏恩 WANG Yun-xia;WANG Dan-xia;JIA Hong-en(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西晋中030024

出　　处：《数学的实践与认识》2021年第15期225-235,共11页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(201901D111123)。

摘　　要：本文研究了具有对数势的粘性Allen-Cahn方程的有限元算法.首先对于对数势函数,通过正则化思想,将函数F(u)的定义域从(-1,1)扩展到(-∞,∞);其次提出了一种新的数值格式,即在空间上采用混合有限元方法进行离散,时间上采用二阶格式进行离散;然后证明了该数值方法是无条件能量稳定的,且对其误差估计作了详细的分析;最后给出了一些数值算例,验证了该方法的有效性.A novel finite element method for solving viscous Allen-Cahn equation with logarithmic potential is constructed in this paper.Firstly,for the logarithmic potential function,the domain of the function F(u) is extended from(-1,1) to(-∞,∞) by regularization.Secondly,a new numerical scheme is proposed,that is,the mixed finite element method is used for discretization in the space and the second order scheme is adopted for discretization in the time.Then the unconditional energy stability of the numerical method is proved theoretically and the error estimates are analyzed in detail.Finally,some numerical examples are given to verify the effectiveness of the proposed method.

关 键 词：对数势 粘性Allen-Cahn方程 混合有限元方法 能量稳定 

分 类 号：O241.82[理学—计算数学]