论文标题
Cahn-Hilliard方程的基于GPAV的无条件能量稳定方案：稳定性和误差分析
gPAV-Based Unconditionally Energy-Stable Schemes for the Cahn-Hilliard Equation: Stability and Error Analysis
论文作者
论文摘要
我们为Cahn-Hilliard方程提供了几种一阶和二阶数值方案，具有离散的无条件能量稳定性。这些方案源于广义阳性辅助变量（GPAV）的想法，仅需要具有恒定系数矩阵的线性代数系统的解决方案。更重要的是，这些方案的计算复杂性（每次时间步长）约为GPAV的一半，而标量辅助变量（SAV）方法（在以前的工作中）。我们研究了所提出的方案的稳定性，以建立现场函数和辅助变量的稳定性界限，并提供其误差分析。提出了数值实验以验证理论分析，并且还证明了在很大时间步进尺寸的方案的稳定性。
We present several first-order and second-order numerical schemes for the Cahn-Hilliard equation with discrete unconditional energy stability. These schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and require only the solution of linear algebraic systems with a constant coefficient matrix. More importantly, the computational complexity (operation count per time step) of these schemes is approximately a half of those of the gPAV and the scalar auxiliary variable (SAV) methods in previous works. We investigate the stability properties of the proposed schemes to establish stability bounds for the field function and the auxiliary variable, and also provide their error analyses. Numerical experiments are presented to verify the theoretical analyses and also demonstrate the stability of the schemes at large time step sizes.
