A stabilized finite volume element method for solving Poisson-Nernst-Planck equations.

One difficulty in solving the Poisson-Nernst-Planck (PNP) equations used for studying the ion transport in channel proteins is the possible convection-dominant problem in the Nernst-Planck equations. In this paper, to overcome this issue, considering the general mixed boundary conditions of concentration functions on the interface, a novel stabilized finite volume element method based on the standard weak formulation to solve the steady-state PNP equations is proposed and analyzed. Numerical tests on four ion-channel proteins served as benchmark with varying boundary conditions in a certain range show that the new stabilized technique not only improves the robustness of the new PNP solver, but also makes the computed (especially the maximal) concentration values much more reasonable.