Numerical Approximations and Error Analysis of the Cahn–Hilliard Equation with Reaction Rate Dependent Dynamic Boundary Conditions

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→ 0 and K→∞ 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.