Abstract: The virtual element method was used to solve a three-dimensional steady-state Poisson-Nernst-Planck (PNP) equations on polyhedral meshes. The virtual element discrete forms of the PNP equations were given, and the matrix expressions of the stiffness matrix and the load vector of the electric potential equation and ion concentration equation were derived. The numerical experimental results show that the virtual element computation of PNP equations is realized in three different polyhedral meshes, and the numerical solutions reach the optimal order in both L² and H² norms.

Key words: Poisson-Nernst-Planck equation, virtual element method, polyhedral mesh, three-dimension