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Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations

Hailiang Liu Iowa State University, Department of Mathematics, Ames, IA 50011, USA Zhongming Wang Florida International University, Department of Mathematics and Statistics, Miami, FL 33199, USA Peimeng Yin Wayne State University, Department of Mathematics, Detroit, MI 48202, USA Hui Yu Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, China

Numerical Analysis and Scientific Computing mathscidoc:2205.25017

Journal of Computational Physics, 452, (1), 110777, 2022.3
In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson–Nernst–Planck (PNP) equations, which have found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve the positivity of cell averages at all time steps. The positivity of numerical solutions is then restored by a scaling limiter in reference to positive weighted cell averages. The method is also shown to preserve steady states. Numerical examples are presented to demonstrate the third order accuracy and illustrate the positivity-preserving property in both one and two dimensions.
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@inproceedings{hailiang2022positivity-preserving,
  title={Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations},
  author={Hailiang Liu, Zhongming Wang, Peimeng Yin, and Hui Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520141422622485302},
  booktitle={Journal of Computational Physics},
  volume={452},
  number={1},
  pages={110777},
  year={2022},
}
Hailiang Liu, Zhongming Wang, Peimeng Yin, and Hui Yu. Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations. 2022. Vol. 452. In Journal of Computational Physics. pp.110777. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520141422622485302.
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