# The Poisson-Boltzmann Equation: Analysis, A Posteriori Error Estimates and Applications

## Dr. Svetoslav Nakov

**May 7, 2019, 1:30 p.m. S2 416-1**

The Poisson-Boltzmann equation (PBE) gives a mean field description of the electrostatic potential in a system of molecules in ionic solution. It is a commonly accepted and widely used approach to the modelling of the electrostatic fields in and around biological macromolecules such as proteins, RNA or DNA.

This work is devoted to the existence and uniqueness analysis of the PBE and the derivation of a posteriori estimates for the distance between its exact solution and any admissible approximation of it. These error estimates allow for the construction of adaptive finite element methods for the fully reliable solution of the PBE in large systems with complicated molecular geometries and distribution of charges. More precisely, we derive two types of a posteriori error estimates: global estimates for the error in the electrostatic potential, measured in the so called energy norm, and goal oriented error estimates for the electrostatic interaction between molecules.