Error Analysis of Mixed Finite Element Method for Poisson-Nernst-Planck System

To improve the convergence rate in L-2 norm from suboptimal to optimal for both electrostatic potential and ionic concentrations in Poisson-Nernst-Planck (PNP) system, we propose the mixed finite element method in this article to discretize the electrostatic potential equation, and still use the standard finite element method to discretize the time-dependent ionic concentrations equations. Optimal error estimates in L-infinity ([0, T]; L-2) norm for the electrostatic potential, and in L-infinity ([0, T]; L-2) and L-infinity ([0, T]; H-1) norms for the ionic concentrations are attained. As a by-product, the electric field can also achieve a higher approximation order in contrast with the standard finite element method for PNP system. Numerical experiments are performed to validate the theoretical results. (c) 2017 Wiley Periodicals, Inc.