@Article{CiCP-26-5,
author = {Xiao, Li and Lili, Ju and Xucheng, Meng},
title = {Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation},
journal = {Communications in Computational Physics},
year = {2019},
volume = {26},
number = {5},
pages = {1510--1529},
abstract = {<p style="text-align: justify;">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<sup>∞</sup> 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<sup>∞</sup> boundedness is usually needed.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2019.js60.12},
url = {https://global-sci.com/article/79868/convergence-analysis-of-exponential-time-differencing-schemes-for-the-cahn-hilliard-equation}
}