Finite element approximation to a finite-size modified poisson-boltzmann equation

Jehanzeb Hameed Chaudhry, Stephen D. Bond, Luke N. Olson

Research output: Contribution to journalArticlepeer-review


The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson- Boltzmann equation in the limit of zero-size ions. Moreover, the modified equation fits well into existing finite element frameworks for the Poisson-Boltzmann equation. In this paper, we advocate a wider use of the modified equation and establish well-posedness of the weak problem along with convergence of an associated finite element formulation.We also examine several practical considerations such as conditioning of the linearized form of the nonlinear modified Poisson-Boltzmann equation, implications in numerical evaluation of the modified form, and utility of the modified equation in the context of the classical Poisson- Boltzmann equation.

Original languageEnglish (US)
Pages (from-to)347-364
Number of pages18
JournalJournal of Scientific Computing
Issue number3
StatePublished - Jun 2011


  • Finite elements
  • Poisson-Bikerman
  • Poisson-Boltzmann

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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