粘性Cahn-Hilliard方程的二阶稳定Crank-Nicolson-Leapfrog格式  

A Stable Second-Order Crank-Nicolson-Leapfrog Scheme for the Viscous Cahn-Hilliard Equation

作　　者：刘静[1] 王旦霞[1] 王李靖 

机构地区：[1]太原理工大学数学系,山西 晋中

出　　处：《应用数学进展》2023年第1期339-351,共13页Advances in Applied Mathematics

摘　　要：本文研究了粘性Cahn-Hilliard方程的一个二阶逼近。对于双阱势函数,本文通过引入拉格朗日乘子得到一个等价形式。其次,使用Crank-Nicolson-Leapfrog格式进行时间离散,使用有限元方法进行空间离散,从而得出了一个二阶线性无条件稳定的数值格式。然后,证明了数值格式的无条件能量稳定性和误差分析。最后,给出了几个数值模拟,验证了格式的数值精度。In this paper, we present a second-order approximation of the viscous Cahn-Hilliard equation. Firstly, an equivalent form of the system has been obtained by introducing a Lagrange multiplier for the double-well potential function. Secondly, a second-order linear unconditionally stable numerical scheme is proposed by using the Crank-Nicolson-Leapfrog scheme and mixed finite element method, respectively, to discrete the time and space. Furthermore, we prove that the scheme is second-order convergent. Finally, numerical examples are performed to show that the numerical accuracy of the proposed scheme is accurate and effective.

关 键 词：粘性Cahn-Hilliard Crank-Nicolson-Leapfrog 无条件稳定 误差估计 

分 类 号：O17[理学—数学]