@Article{CiCP-25-703,
author = {Xiaofeng Yang and Jia Zhao},
title = {On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {3},
pages = {703--728},
abstract = {<p style="text-align: justify;">In this paper, we consider numerical approximations for the fourth-order
Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic
Flory-Huggins bulk potential. One numerical challenge in solving such system
is how to develop proper temporal discretization for nonlinear terms in order to preserve
its energy stability at the time-discrete level. We overcome it by developing a
set of first and second order time marching schemes based on a newly developed &quot;Invariant
Energy Quadratization&quot; approach. Its novelty is producing linear schemes,
by discretizing all nonlinear terms semi-explicitly. We further rigorously prove all
proposed schemes are unconditionally energy stable. Various 2D and 3D numerical
simulations are presented to demonstrate the stability, accuracy, and efficiency of the
proposed schemes thereafter.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0259},
url = {http://global-sci.org/intro/article_detail/cicp/12826.html}
}