A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.

翻译：本文针对光滑区域中具有Cahn-Hilliard型动态边界条件的Cahn-Hilliard方程全离散格式，给出了最优阶误差估计的证明。该数值方法在空间上采用线性体-表面有限元离散，在时间上采用1至5阶线性隐式后向差分公式。研究证明了最优阶误差估计的成立。误差估计基于抽象框架下的一致性与稳定性分析，其核心在于利用二阶系统反对称结构的能量估计方法。