论文标题
具有动态边界条件的Cahn-Hilliard方程的数值近似和误差分析
Numerical Approximations and Error Analysis of the Cahn-Hilliard Equation with Dynamic Boundary Conditions
论文作者
论文摘要
我们考虑具有动态边界条件的Cahn-Hilliard方程的数值近似值（C. Liuet。，Arch。ConationMech。Anal。，2019）。我们提出了一个时代，线性和能量稳定数值方案的一阶，该方案基于稳定的线性隐式方法。证明了该方案的能量稳定性，并进行了半差异误差估计。进行数值实验，包括与以前的工作的比较，相对于时间步长和液滴的形状变形的精度测试，以验证所提出的方案的准确性和稳定性。
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational 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.
