Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

@article{Chen2019PositivitypreservingES,
  title={Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential},
  author={Wenbin Chen and Cheng Wang and Xiaoming Wang and Steven M. Wise},
  journal={J. Comput. Phys. X},
  year={2019},
  volume={3},
  pages={100031}
}
We present and analyze finite difference numerical schemes for the Allen Cahn/Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both the first order and second order accurate temporal algorithms are considered. In the first order scheme, we treat the nonlinear logarithmic terms and the surface diffusion term implicitly, and update the linear expansive term and the mobility explicitly. We provide a theoretical justification that, this numerical algorithm has a unique… Expand
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