Title：Finite Element Methods for Poisson-Nernst-Planck Equations and Application to Ion Channels
Speaker：Pengtao Sun, Ph.D. ， Associate Professor of Mathematics，University of Nevada Las Vegas
The Poisson-Nernst-Planck (PNP) system is one of commonly used models in theoretical and computational studies of biological ion channels, especially the fields of electro-kinetics and electro-hydrodynamics gained an increasing interest in recent years. In contrast to the limited amount of work on the numerical analysis, numerical computations with PNP equations have been widely conducted by computational physicists and biophysicists, and finite element method is most popularly adopted in recent years to solve the steady-state and time-dependent PNP equations. However, the finite element analyses of PNP equations are either incomplete or lack the accuracy. In this talk, I am going to address the challenging problems in the finite element analysis of PNP equations, then introduce our recent work on the a priori finite element error analysis for the time-dependent PNP equations, including both standard Galerkin method and mixed finite element method. We also developed and analyzed the mixed finite element method for PNP/Stokes coupling problem. Finally, I will introduce the application of PNP system to ion channels, and our future research plan on a realistic ionic fluid problem modeled by the transient PNP/Stokes coupling system.