We consider the numerical approximations of the Cahn–Hilliard equation with dynamic boundary conditions [C. Liu et al., Arch. Ration. Mech. Anal., 2019]. We propose a first-order in time, linear and energy-stable numerical scheme, which is based on the stabilized linearly implicit approach. The energy stability of the scheme is proved and the semi-discrete-in-time error estimates are carried out. Numerical experiments, including the comparison with the former work, the accuracy tests with respect to the time step size and the shape deformation of a droplet, are performed to validate the accuracy and the stability of the proposed scheme.

中文翻译：

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具有动态边界条件的Cahn-Hilliard方程的数值逼近和误差分析

我们考虑了带有动态边界条件的Cahn-Hilliard方程的数值逼近[C。Liu等，Arch。配给。机甲。肛门 ，2019]。我们提出了基于稳定线性隐式方法的一阶时间，线性和能量稳定的数值方案。证明了该方案的能量稳定性，并进行了半离散时间误差估计。进行了数值实验，包括与先前工作的比较，关于时间步长大小和液滴形状变形的准确性测试，以验证所提出方案的准确性和稳定性。