Abstract: We gave a discretized form of edge-averaged finite element for a class of three-dimensional Poisson-Nernst-Planck equations. Under appropriate grid conditions, the total stiffness matrix obtained by the discrete form was an M-matrix, which ensured the non-negative properties of the numerical solution. The numerical experimental results show that compared with the standard finite element method, the edge-averaged finite element method has shorter CPU time and less error.

Key words: Poisson-Nernst-Planck equations, edge-averaged finite element method, finite element method