A Posteriori Analysis and Efficient Refinement Strategies for the Poisson-Boltzmann Equation
For researchers solving the Poisson-Boltzmann equation numerically, this work provides a method to accurately quantify and reduce errors in solvation free energy calculations.
The paper uses adjoint-based a posteriori analysis to quantify errors in solvation free energy from finite element solutions of the Poisson-Boltzmann equation, and proposes novel refinement strategies to reduce these errors.
The Poisson-Boltzmann equation (PBE) models the electrostatic interactions of charged bodies such as molecules and proteins in an electrolyte solvent. The PBE is a challenging equation to solve numerically due to the presence of singularities, discontinuous coefficients and boundary conditions. Hence, there is often large error in the numerical solution of the PBE that needs to be quantified. In this work, we use adjoint based a posteriori analysis to accurately quantify the error in an important quantity of interest, the solvation free energy, for the finite element solution of the PBE. We identify various sources of error and propose novel refinement strategies based on a posteriori error estimates.