  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.
