Year: 2021
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 31–60
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2020-0003
Annals of Applied Mathematics, Vol. 37 (2021), Iss. 1 : pp. 31–60
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Cahn-Hilliard equation logarithmic kernel semi-implicit scheme energy stability.