We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized approach. The corresponding energy stability and convergence analysis of the scheme are derived theoretically. Some numerical experiments are performed to verify the effectiveness and accuracy of the second-order numerical scheme, including numerical simulations under various initial conditions and energy potential functions, and comparisons with the literature works.
翻译:我们用动态边界条件研究Cahn-Hilliard等式的数字算法和误差分析,提出了时间的第二顺序、线性和能源稳定办法,这是第一级稳定办法的延伸,从理论上推导出该办法相应的能源稳定性和趋同分析,进行了一些数字实验,以核查第二级数字办法的有效性和准确性,包括在各种初始条件和能源潜力功能下进行的数字模拟,以及与文学作品的比较。