Superconvergence analysis of finite element method for Poisson–Nernst–Planck equations

Abstract

This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By employing high accuracy integral identities together with mean value technique, the superclose estimates in H1‐norm are derived for the semi‐discrete and the backward Euler fully‐discrete schemes, which improve the suboptimal error estimate in L2‐norm in the previous literature. Furthermore, the global superconvergence results in H1‐norm are obtained through interpolation postprocessing approach. Finally, a numerical example is provided to confirm the theoretical analysis.