姚廷富, 李顺利. 基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析[J]. 华南师范大学学报(自然科学版), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
引用本文: 姚廷富, 李顺利. 基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析[J]. 华南师范大学学报(自然科学版), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
YAO Tingfu, LI Shunli. An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099
Citation: YAO Tingfu, LI Shunli. An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(6): 90-96. doi: 10.6054/j.jscnun.2020099

基于能量不变二次化法的Cahn-Hilliard方程的数值误差分析

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

  • 摘要: 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.

     

    Abstract: 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.

     

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