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 - <p style="text-align: justify;">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.</p>