An Adaptive Conservative Finite Volume Method for Poisson-Nernst-Planck Equations on a Moving Mesh

In this paper, we present a finite volume method for solving Poisson-Nernst-Planck (PNP) equations in one spatial dimension. To reduce computational cost, an adaptive moving mesh strategy is employed in order to resolve thin Debye layers near the boundary. In addition to the standard monitor functions, we propose two new ones for the moving mesh partial differential equations to improve the accuracy of the numerical solution. The method guarantees the strict mass conservation. We have proved that the scheme maintains positivity on the adaptive moving mesh which has not been done for PNP.