Second-Order Linear Stabilized Semi-Implicit Crank-Nicolson Scheme for the Cahn-Hilliard Model with Dynamic Boundary Conditions
Year: 2025
Author: Xiangjun Meng, Xuelian Bao, Zhengru Zhang
Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 137–170
Abstract
We propose a kind of second-order stabilized Crank-Nicolson scheme which can be applied to three types of Cahn-Hilliard model with dynamic boundary conditions. We give the corresponding proof of stability and convergence theoretically which takes the reaction rate dependent dynamic boundary conditions as an example. We verify the effectiveness and universality of our proposed scheme by conducting some typical numerical simulations and comparing with the literature works. It’s found that second-order scheme takes much less CPU time than the first-order scheme to reach the same final time.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0269
Communications in Computational Physics, Vol. 37 (2025), Iss. 1 : pp. 137–170
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Cahn-Hilliard equation dynamic boundary conditions reaction rate second-order Crank-Nicolson formula energy stability convergence analysis.