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∞(H1)L∞(H1) and L2(H1)L2(H1) norms, and suboptimal error estimates in L∞(L2)L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2)L∞(L2) 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.