A First-Order System Least-Squares Finite Element Method for the Poisson-Boltzmann Equation

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 I. methanol, and a dipole, which highlights robustness of our approach. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 31: 1625-1635, 2010