粘性Cahn-Hilliard方程Crank-Nicolson/Adams-Bashforth格式的混合有限元方法

Crank-Nicolson/Adams-Bashforth Scheme of Mixed Finite Element Method for the Viscous Cahn-Hilliard Equation

本文基于线性的Crank-Nicolson/Adams-Bashforth格式,建立了有效稳定的数值算法求解粘性Cahn-Hilliard方程。在该算法中,非线性体积力被显示处理,导致求解具有常系数的线性系统,从而提高算法效率。此外,该算法的稳定性以及误差估计被详细证明。最终,通过数值实验证明了该格式的稳定性及收敛阶。

In this paper, an efficient stabilized algorithm based on the linear Crank-Nicolson/Adams-Bashforth scheme is proposed to solve the viscous Cahn-Hilliard equation. In this algorithm, the nonlinear bulk force is treated explicitly with linear stabilization term. This treatment leads to solve linear systems with constant coefficients that can improve algorithm efficiency. Further, the stability analysis and priori error estimates on proposed method are provided in detail. Finally, a series of numerical experiments are implemented to illustrate the theoretical analysis.