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Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation

Huailing Song Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25016

Journal of Scientific Computing, 73, 1178-1203, 2017
In this article, we present a second-order in time implicit-explicit (IMEX) local discontinuous Galerkin (LDG) method for computing the Cahn-Hilliard equation, which describes the phase separation phenomenon. It is well-known that the Cahn-Hilliard equation has a nonlinear stability property, i.e., the free-energy functional decreases with respect to time. The discretized Cahn-Hilliard system modeled by the IMEX LDG method can inherit the nonlinear stability of the continuous model. We apply a stabilization technique and prove unconditional energy stability of our scheme. Numerical experiments are performed to validate the analysis. Computational efficiency can be significantly enhanced by using this IMEX LDG method with a large time step.
local discontinuous Galerkin method; implicit-explicit; second-order; stability analysis; the Cahn-Hilliard equation
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@inproceedings{huailing2017unconditional,
  title={Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation},
  author={Huailing Song, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416102719947917051},
  booktitle={Journal of Scientific Computing},
  volume={73},
  pages={1178-1203},
  year={2017},
}
Huailing Song, and Chi-Wang Shu. Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation. 2017. Vol. 73. In Journal of Scientific Computing. pp.1178-1203. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416102719947917051.
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