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Volume 5, Issue 1
An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations

Ying Yang & Benzhuo Lu

DOI: 10.4208/aamm.11-m11184

Adv. Appl. Math. Mech., 5 (2013), pp. 113-130.

Published online: 2013-05

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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

Poisson-Nernst-Planck equations, finite element method, error bounds.

  • AMS Subject Headings

65N30, 92C40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-113, author = {Yang , Ying and Lu , Benzhuo}, title = {An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m11184}, url = {http://global-sci.org/intro/article_detail/aamm/60.html} }
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.

Yang , Ying and Lu , Benzhuo. (2013). An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations. Advances in Applied Mathematics and Mechanics. 5 (1). 113-130. doi:10.4208/aamm.11-m11184
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