Premium
A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation
Author(s) -
Bond Stephen D.,
Chaudhry Jehanzeb Hameed,
Cyr Eric C.,
Olson Luke N.
Publication year - 2010
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.21446
Subject(s) - poisson–boltzmann equation , finite element method , a priori and a posteriori , estimator , mathematics , least squares function approximation , poisson's equation , mathematical optimization , mathematical analysis , physics , ion , philosophy , statistics , epistemology , quantum mechanics , thermodynamics
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. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010