In this paper, we construct several efficient scalar auxiliary variable (SAV) schemes based on the Fourier-spectral method in space for the Cahn-Hilliard-Hele-Shaw system. The temporal discretizations are built upon the first-order Euler and second-order BDF method, respectively. We derive the unconditional energy stability for both schemes and also establish the rigorous error estimates for the first-order SAV Fourier-spectral scheme. Finally, various numerical experiments are presented to demonstrate the accuracy and performance for the constructed schemes.

中文翻译：

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Cahn-Hilliard-Hele-Shaw系统SAV傅里叶谱方法的误差分析

在本文中，我们基于空间傅里叶谱方法为 Cahn-Hilliard-Hele-Shaw 系统构建了几种有效的标量辅助变量 (SAV) 方案。时间离散化分别建立在一阶欧拉和二阶 BDF 方法之上。我们推导出两种方案的无条件能量稳定性，并为一阶 SAV 傅立叶谱方案建立严格的误差估计。最后，提出了各种数值实验来证明所构建方案的准确性和性能。