TY - JOUR T1 - Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation AU - Li , Xiao AU - Ju , Lili AU - Meng , Xucheng JO - Communications in Computational Physics VL - 5 SP - 1510 EP - 1529 PY - 2019 DA - 2019/08 SN - 26 DO - http://doi.org/10.4208/cicp.2019.js60.12 UR - https://global-sci.org/intro/article_detail/cicp/13274.html KW - Cahn-Hilliard equation, exponential time differencing, convergence analysis, uniform $L^∞$ boundedness. AB -

In this paper, we rigorously prove the convergence of fully discrete first- and second-order exponential time differencing schemes for solving the Cahn-Hilliard equation. Our analyses mainly follow the standard procedure with the consistency and stability estimates for numerical error functions, while the technique of higher-order consistency analysis is adopted in order to obtain the uniform L boundedness of the numerical solutions under some moderate constraints on the time step and spatial mesh sizes. This paper provides a theoretical support for numerical analysis of exponential time differencing and other related numerical methods for phase field models, in which an assumption on the uniform L boundedness is usually needed.