Volume 37, Issue 1
Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials

Dong LiTao Tang

Ann. Appl. Math., 37 (2021), pp. 31-60.

Published online: 2021-02

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  • 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.


  • Keywords

Cahn-Hilliard equation, logarithmic kernel, semi-implicit scheme, energy stability.

  • AMS Subject Headings

65M60, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

madli@ust.hk (Dong Li)

  • BibTex
  • RIS
  • TXT
@Article{AAM-37-31, author = {Li , Dong and Tang , Tao}, title = {Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {37}, number = {1}, pages = {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.


}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2020-0003}, url = {http://global-sci.org/intro/article_detail/aam/18630.html} }
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 -

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.


Dong Li & Tao Tang. (1970). Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials. Annals of Applied Mathematics. 37 (1). 31-60. doi:10.4208/aam.OA-2020-0003
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