“…In this paper, we focus on the superconvergence analysis of bilinear finite element method (FEM) for the nonlinear Planck–Nernst–Poisson (PNP) equations , which describes the mass concentration of particles and the electrostatic potential ψ : (0, T ] → ℝ, satisfying where Ω ⊂ ℝ 2 is a rectangular domain with its boundary ∂Ω , and F i ( i = 1, 2, 3) are the reaction terms.…”