Local averaging type a posteriori error estimates for the nonlinear steady-state Poisson-Nernst–Planck equations

Abstract The a posteriori error estimates are studied for a class of nonlinear stead-state Poisson-Nernst–Planck equations, which are a coupled system consisting of the Nernst–Planck equation and the Poisson equation. Both the global upper bounds and the local lower bounds of the error estimators are obtained by using a local averaging operator. Numerical experiments are given to confirm the reliability and efficiency of the error estimators.