In this paper, we develop two linear and unconditionally energy stable Fourier‐spectral schemes for solving viscous Cahn–Hilliard equation based on the recently scalar auxiliary variable approach. The temporal discretizations are built upon the first‐order Euler method and second‐order Crank–Nicolson method, respectively. We carry out the energy stability and error analysis rigorously. Various classical numerical experiments are performed to validate the efficiency and accuracy of the proposed schemes.

中文翻译：

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粘性Cahn-Hilliard方程的标量辅助变量傅里叶谱方法的能量稳定性和收敛性

在本文中，我们基于最近的标量辅助变量方法，开发了两种线性且无条件的能量稳定傅里叶谱方案，用于求解粘性Cahn-Hilliard方程。时间离散化分别基于一阶Euler方法和二阶Crank-Nicolson方法。我们严格进行能量稳定性和误差分析。进行了各种经典的数值实验，以验证所提出方案的效率和准确性。