Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation (Communications in Computational Physics, 2019)
In this paper, we rigorously prove the convergence of fully discrete first- and second-order exponential time differencing schemes for solving the Cahn-Hilliardequation. Our analyses mainly follow the standard procedure with the consistency andstability estimates for numerical error functions, while the technique of higher-orderconsistency analysis is adopted in order to obtain the uniform L∞ boundedness ofthe numerical solutions under some moderate constraints on the time step and spatialmesh 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.