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) system , which has found much use in diverse applications. For the arbitrary high order DG method introduced in H. Liu and Z. Wang, J. Comput. Phys., 328, 2017%DIFDELCMD < ]%%% , solution positivity is only numerically enforced. In this paper we design a novel DG method, which with Euler forward time discretization is shown to preserve  positivity of cell averages at all time steps. Positivity of numerical solutions is then restored by a scaling limiter in reference to positive cell averages . Numerical examples are presented to demonstrate the third order accuracy and illustrate the positivity-preserving property in both one and two dimensions.
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 has found much use in diverse applications. %DIFDELCMD < ]%%% 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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system
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For the arbitrary high order DG method introduced in
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H. Liu and Z. Wang, J. Comput. Phys., 328, 2017
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, solution positivity is only numerically enforced. In this paper we design a novel DG method, which
Our DG method
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the
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Positivity
The positivity
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cell averages
weighted cell averages. The method is also shown to preserve steady states