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.

翻译：我们考虑了Cahn-Hilliard方程式的数字近似值和误差分析,以及反应率取决于动态边界条件(P.Knopf等人,arXiv,2020年)。根据稳定的线性隐含方法,提出了解决这一模型的第一阶时间、线性和能源稳定办法。还得出了相应的半分解时误差估计数。进行了数值实验,包括与以前工作的比较,放松参数K\rightror0$和$K\rightrowr\infty$的趋同结果,以及时间步骤大小的精确度测试,以验证拟议方案和误差分析的准确性。