基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析

基于能量不变二次化方法，构造了一个求解Cahn-Hilliard方程的线性数值格式，该线性数值格式对非线性项半显式处理，每步迭代相应的半离散化方程只需要求解一个线性方程；证明了该线性数值格式是无条件能量稳定的，而且是唯一可解的；讨论了该线性数值格式在时间方向的误差估计.数值例子表明:该线性数值格式的数值解在时间方向上基本达到二阶精度, 能够有效模拟相位变化过程.

An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach

A novel linear numerical scheme for the Cahn-Hilliard equation is constructed with the invariant energy quadratization approach. All nonlinear terms in this scheme are treated semi-explicitly and the resulting semi-discrete equation forms a linear system at each time step. It is proved that the proposed scheme is energy-stable unconditionally and solvable uniquely. The error estimate of the numerical scheme for the Cahn-Hilliard equation is discussed. Numerical examples show that the numerical solution of the linear numerical scheme basically achieves the second-order accuracy in the time direction and can effectively simulate the phase change process.