Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials
Numerical Analysis
2021-06-21 v1 Numerical Analysis
Analysis of PDEs
Abstract
We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. We employ the standard semi-implicit numerical 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.
Cite
@article{arxiv.2106.09903,
title = {Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials},
author = {Dong Li and Tao Tang},
journal= {arXiv preprint arXiv:2106.09903},
year = {2021}
}
Comments
23 pages