TY - JOUR
T1 - Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials
AU - Li , Dong
AU - Tang , Tao
JO - Annals of Applied Mathematics
VL - 1
SP - 31
EP - 60
PY - 2021
DA - 2021/02
SN - 37
DO - http://doi.org/10.4208/aam.OA-2020-0003
UR - https://global-sci.org/intro/article_detail/aam/18630.html
KW - Cahn-Hilliard equation, logarithmic kernel, semi-implicit scheme, energy stability.
AB - <p style="text-align: justify;">We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. We employ the standard semi-implicit numerical&nbsp; scheme, which treats the linear fourth-order dissipation term implicitly and the nonlinear term explicitly. Under natural constraints on the time step we prove strict phase separation and energy stability of the semi-implicit scheme. This appears to be the first rigorous result for the semi-implicit discretization of the Cahn-Hilliard equation with singular potentials.</p>