Stephen D. Bond, Jehanzeb Hameed Chaudhry, Eric C. Cyr and Luke N. Olson, A First-Order Systems Least-Squares Finite Element Method for the Poisson-Boltzmann Equation, Journal of Computational Chemistry (2009) in press.

The Poisson-Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this paper, 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.

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@article{BCCO2009,
  author  = {Stephen D. Bond and Jehanzeb Hameed Chaudhry and Eric C. Cyr and
	     Luke N. Olson},
  title   = {A First-Order Systems Least-Squares Finite Element Method for
	     the Poisson-Boltzmann Equation},
  journal = {Journal of Computational Chemistry},
  year	  = 2009,
  pages   = {in press}
}