Error analysis of finite element method for Poisson-Nernst-Planck equations

In this paper we study the a priori error estimates of finite element method for the system of time-dependent Poisson-Nernst-Planck equations, and for the first time, we obtain its optimal error estimates in L ∞ ( H 1 ) and L 2 ( H 1 ) norms, and suboptimal error estimates in L ∞ ( L 2 ) norm, with linear element, and optimal error estimates in L ∞ ( L 2 ) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.