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

Ying Yang and Benzhuo Lu

10.4208/aamm.11-m11184

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

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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.

  • History

Published online: 2013-05

  • AMS Subject Headings

65N30, 92C40

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