@Article{CiCP-11-1261,
author = {Zhengru Zhang and Zhonghua Qiao},
title = {An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {4},
pages = {1261--1278},
abstract = {<p style="text-align: justify;">This paper studies the numerical simulations for the Cahn-Hilliard equation which describes a phase separation phenomenon. The numerical simulation of the
Cahn-Hilliard model needs very long time to reach the steady state, and therefore large
time-stepping methods become useful. The main objective of this work is to construct
the unconditionally energy stable finite difference scheme so that the large time steps
can be used in the numerical simulations. The equation is discretized by the central
difference scheme in space and fully implicit second-order scheme in time. The proposed scheme is proved to be unconditionally energy stable and mass-conservative.
An error estimate for the numerical solution is also obtained with second order in
both space and time. By using this energy stable scheme, an adaptive time-stepping
strategy is proposed, which selects time steps adaptively based on the variation of the
free energy against time. The numerical experiments are presented to demonstrate the
effectiveness of the adaptive time-stepping approach.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.300810.140411s},
url = {http://global-sci.org/intro/article_detail/cicp/7410.html}
}