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arXiv · 2106.09903

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

Dong Li·Tao Tang
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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.

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Dong Li, Tao Tang. 2021-06-18. Stability of the semi-implicit method for the Cahn-Hilliard equation with logarithmic potentials. https://doi.org/10.4208/aam.oa-2020-0003

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