Reliable computer simulation methods for electrostatic biomolecular models based on the Poisson-Boltzmann equation

TL;DR

This paper develops explicit error bounds and indicators for the nonlinear Poisson-Boltzmann equation, enabling reliable adaptive finite element simulations of electrostatic biomolecular models.

Contribution

It introduces computable error bounds and indicators specifically for the nonlinear Poisson-Boltzmann equation, enhancing simulation accuracy.

Findings

Derived explicit error bounds in energy norms.

Developed efficient error indicators for adaptive algorithms.

Facilitated reliable finite element simulations of biomolecular electrostatics.

Abstract

In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can serve as a basis for a reliable adaptive finite element algorithm.