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 - <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>