Mixed finite element analysis for the Poisson-Nernst-Planck/Stokes coupling

In this paper, a type of mixed finite element method is developed to solve the Poisson-Nernst-Planck/Stokes coupling problem which is adopted to model charged fluids through the transport coupling between Stokes equations of an incompressible fluid and Poisson Nernst-Planck (PNP) equations of a diffuse charge system. The Taylor-Hood (Pk+1Pk) mixed element is employed to discretize both mixed Poisson equations and Stokes equations, and the standard P-k finite element is used to discretize Nernst-Planck equations. Optimal convergence rates for both the electrostatic potential and ionic concentrations of PNP equations are obtained in both L-2 and H-1 norms, simultaneously, optimal convergence rates are also obtained for the velocity and pressure of Stokes equations in [H-1](d) and L-2 norm, respectively. Numerical experiments validate the theoretical results. (C) 2018 Elsevier B.V. All rights reserved.