Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation
<|reference_start|>Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation: We propose and analyze a novel approach to construct structure preserving approximations for the Poisson-Nernst-Planck equations, focusing on the positivity preserving and mass conservation properties. The strategy consists of a standard time marching step with a projection (or correction) step to satisfy the desired physical constraints (positivity and mass conservation). Based on the $L^2$ projection, we construct a second order Crank-Nicolson type finite difference scheme, which is linear (exclude the very efficient $L^2$ projection part), positivity preserving and mass conserving. Rigorous error estimates in $L^2$ norm are established, which are both second order accurate in space and time. The other choice of projection, e.g. $H^1$ projection, is discussed.   Numerical examples are presented to verify the theoretical results and demonstrate the efficiency of the proposed method.<|reference_end|>
@article{tong2024positivity,
    title={Positivity preserving and mass conservative projection method for the
  Poisson-Nernst-Planck equation},
    author={Fenghua Tong and Yongyong Cai},
    journal={arXiv preprint arXiv:2403.04291},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04291},
    primaryClass={math.NA cs.NA}
}