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

An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations
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Year:    2013

Author:    Ying Yang, Benzhuo Lu

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 1 : pp. 113–130

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.11-m11184

Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 1 : pp. 113–130

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Poisson-Nernst-Planck equations finite element method error bounds.

Author Details

Ying Yang

Benzhuo Lu

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