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
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。
Abstract: 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.
文章引用：刘静, 王旦霞, 王李靖. 粘性Cahn-Hilliard方程的二阶稳定Crank-Nicolson-Leapfrog格式[J]. 应用数学进展, 2023, 12(1): 339-351. https://doi.org/10.12677/AAM.2023.121037

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