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

Ying Yang & Benzhuo Lu

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

Published online: 2013-05

Preview Full PDF 315 864
Export citation
  • 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

  • Email address
  • References
  • Hide All
    View All

@Article{AAMM-5-113, author = {Ying Yang and Benzhuo Lu}, 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} }
Copy to clipboard
The citation has been copied to your clipboard