2022/06/15 by Xiangjun Meng, Meng, Xiangjun, Xuelian Bao +3 · 1 citation
Materials Science · Mathematics · Engineering · #Solidification and crystal growth phenomena #Differential Equations and Numerical Methods #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.2206.07325
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.