Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials

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.

arXiv comment23 pages

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• On a Class of Sixth-order Cahn-Hilliard Type Equations with Logarithmic Potential
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• On the energy stability of Strang-splitting for Cahn-Hilliard
• The operator-splitting method for Cahn-Hilliard is stable
• Negative time splitting is stable
• An F-modulated stability framework for multistep methods
• On a sinc-type MBE model