Abstract
In this paper, a numerical scheme is proposed and analyzed for Liu-Wu model: Cahn–Hilliard equation with Cahn-Hilliard type dynamic boundary conditions (Liu and Wu, Arch Ration Mech Anal 233(1):167–247, 2019). Inspired by the convex-concave decomposition of the Cahn–Hilliard free energy, prescribed with Neumann boundary condition, we propose a regularized second-order temporal discretization for the coupled PDE system. The unique solvability, unconditional dissipation of a modified free energy and second order convergence analysis (in the
norm) are theoretically established. Finally, several numerical experiments are presented to illustrate the effectiveness of the proposed numerical scheme.