A Decoupling Two-Grid Method for the Steady-State Poisson-Nernst-Planck   Equations
  Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations. 
Ying Yang, Benzhuo Lu and Yan Xie
math.NA