论文标题
具有反应速率依赖性动态边界条件的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 reaction rate dependent dynamic boundary conditions
论文作者
论文摘要
我们考虑具有反应速率依赖性动态边界条件的Cahn-Hilliard方程的数值近似值和误差分析（P. Knopf等，Arxiv，2020）。基于稳定的线性隐式方法，提出了解决此模型的时间，线性和能量稳定的方案。还得出了该方案的相应半差异时间误差估计。数值实验，包括与以前的工作的比较，放松参数$ k \ rightarrow0 $和$ k \ rightarrow \ infty \ infty $的收敛结果以及相对于时间步长的准确性测试，以验证所提出的方案的准确性和错误分析。
We consider numerical approximations and error analysis for the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (P. Knopf et. al., arXiv, 2020). Based on the stabilized linearly implicit approach, a first-order in time, linear and energy stable scheme for solving this model is proposed. The corresponding semi-discretized-in-time error estimates for the scheme are also derived. Numerical experiments, including the comparison with the former work, the convergence results for the relaxation parameter $K\rightarrow0$ and $K\rightarrow\infty$ and the accuracy tests with respect to the time step size, are performed to validate the accuracy of the proposed scheme and the error analysis.
