TY - JOUR T1 - An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations AU - Yang , Ying AU - Lu , Benzhuo JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 113 EP - 130 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.11-m11184 UR - https://global-sci.org/intro/article_detail/aamm/60.html KW - Poisson-Nernst-Planck equations, finite element method, error bounds. AB -

Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. Several numerical examples including biomolecular problems are shown to support our analysis.