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We study the numerical algorithm and error analysis for the Cahn-Hilliardequation with dynamic boundary conditions. A second-order in time, linear andenergy stable scheme is proposed, which is an extension of the first-orderstabilized approach. The corresponding energy stability and convergenceanalysis of the scheme are derived theoretically. Some numerical experimentsare performed to verify the effectiveness and accuracy of the second-ordernumerical scheme, including numerical simulations under various initialconditions and energy potential functions, and comparisons with the literatureworks.

Second order stabilized semi-implicit scheme for the Cahn-Hilliard model with dynamic boundary conditions