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An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

Published online by Cambridge University Press:  03 June 2015

Ying Yang  and
Benzhuo Lu
Ying Yang*
Affiliation:
Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China
Benzhuo Lu*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, the National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
Corresponding author. Email: yangying@lsec.cc.ac.cn
Email: bzlu@lsec.cc.ac.cn
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Abstract

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.

Keywords

65N3092C40Poisson-Nernst-Planck equationsfinite element methoderror bounds
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 113 - 130
Copyright
Copyright © Global-Science Press 2013

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