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| Stability of the Semi-Implicit Method\\ for the Cahn-Hilliard Equation with\\ Logarithmic Potentials |
| Dong Li,Tao Tang |
| (Department of Mathematics, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon, Hong Kong;Division of Science and Technology, BNU-HKBU United International College,
Zhuhai 519087, Guangdong, China; and SUSTech International Center for Mathematics,
Southern University of Science and\\ Technology,
Shenzhen 518055, Guangdong, China) |
| DOI： |
| 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. |
| Key words: Cahn-Hilliard equation, logarithmic kernel, semi-implicit scheme, energy stability. |