@Article{JMS-51-1,
author = {Wang, Lin and Yu, Haijun},
title = {Convergence Analysis of an Unconditionally Energy Stable Linear Crank-Nicolson Scheme for the Cahn-Hilliard Equation},
journal = {Journal of Mathematical Study},
year = {2018},
volume = {51},
number = {1},
pages = {89--114},
abstract = {<p style="text-align: justify;">Efficient and unconditionally stable high order time marching schemes are
very important but not easy to construct for nonlinear phase dynamics. In this paper,
we propose and analysis an efficient stabilized linear Crank-Nicolson scheme for the
Cahn-Hilliard equation with provable unconditional stability. In this scheme the nonlinear
bulk force are treated explicitly with two second-order linear stabilization terms.
The semi-discretized equation is a linear elliptic system with constant coefficients, thus
robust and efficient solution procedures are guaranteed. Rigorous error analysis show
that, when the time step-size is small enough, the scheme is second order accurate in
time with a prefactor controlled by some lower degree polynomial of $1/ \varepsilon.$ Here $\varepsilon$ is the
interface thickness parameter. Numerical results are presented to verify the accuracy
and efficiency of the scheme.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v51n1.18.06},
url = {https://global-sci.com/article/87742/convergence-analysis-of-an-unconditionally-energy-stable-linear-crank-nicolson-scheme-for-the-cahn-hilliard-equation}
}