A virtual element method for the steady-state Poisson-Nernst-Planck equations on polygonal meshes

Abstract Poisson-Nernst-Planck equations are a nonlinear coupled system which are widely used to describe electrodiffusion processes in biomolecular systems and semiconductors, etc. A virtual element method with order k ( k ≥ 1 ) is proposed to numerically approximate the Poisson-Nernst-Planck equations on polygonal meshes. The error estimates in the H 1 norm are presented for the numerical solution to the Poisson-Nernst-Planck equations. Numerical examples show that the virtual element method can work well on general polygonal elements and the numerical results agree with the theoretical prediction.