title: A first-order system least-squares finite element method for the Poisson-Boltzmann equation.
abstract: The Poisson-Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson-Boltzmann equation. We expose the flux directly through a first-order system form of the equation. Using this formulation, we propose a system that yields a tractable least-squares finite element formulation and establish theory to support this approach. The least-squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach.
authors.affiliation: Department of Computer Science, University of Illinois, Urbana, Illinois 61801, USA.
authors.forename: Stephen D
authors.initials: SD
authors.lastname: Bond
authors.forename: Jehanzeb Hameed
authors.initials: JH
authors.lastname: Chaudhry
authors.forename: Eric C
authors.initials: EC
authors.lastname: Cyr
authors.forename: Luke N
authors.initials: LN
authors.lastname: Olson
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004546:Elapid Venoms / Q000737:chemistry; D020342:Finite Element Analysis; D016018:Least-Squares Analysis; D000432:Methanol / Q000737:chemistry; D016012:Poisson Distribution; D055672:Static Electricity
chemical_list: D004546:Elapid Venoms; C044937:fasciculin; D000432:Methanol