Journal of Scientific Computing

, Volume 47, Issue 3, pp 347–364 | Cite as

Finite Element Approximation to a Finite-Size Modified Poisson-Boltzmann Equation

  • Jehanzeb Hameed ChaudhryEmail author
  • Stephen D. Bond
  • Luke N. Olson


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.


Finite elements Poisson-Boltzmann Poisson-Bikerman 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Jehanzeb Hameed Chaudhry
    • 1
    Email author
  • Stephen D. Bond
    • 2
  • Luke N. Olson
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Applied Mathematics and Applications GroupSandia National LaboratoriesAlbuquerqueUSA

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