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

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. Our DG method with Euler forward time discretization is shown to preserve positivity cell averages at all steps. The numerical solutions then restored by a scaling limiter reference positive weighted averages. also steady states. Numerical examples are presented demonstrate accuracy illustrate property both one two dimensions.