We consider numerical approximations and error analysis for the Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions (Knopf et al. ESAIM Math Model Numer Anal 55(1):229–282, 2021). 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 simulations with different energy potentials, the comparison with the former work, the convergence results for the relaxation parameter \(K\rightarrow 0\) 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.

我们考虑了具有依赖于反应速率的动态边界条件的Cahn–Hilliard方程的数值逼近和误差分析（Knopf等人，ESAIM Math Model Numer Anal 55（1）：229–282，2021）。基于稳定的线性隐式方法，提出了求解该模型的时间，线性和能量稳定的一阶方案。还导出了该方案的相应的半离散时间误差估计。数值实验，包括不同能量势的模拟，与前者的比较，松弛参数\（K \ rightarrow 0 \）和\（K \ rightarrow \ infty \）的收敛结果 并进行了有关时间步长的准确性测试，以验证所提出方案和误差分析的准确性。