Nodally bound-preserving discontinuous Galerkin methods for charge transport

Speaker's Name: Alex Trenam
Speaker's Affiliation: Heriot Watt
Speaker's Research Theme(s): Numerical and applied analysis, Applied Mathematics
Abstract:
Ensuring the positivity of density variables is not only important for solutions to remain physically-relevant, but it can also be a crucial factor in the stability of coupled systems describing charge transport. In this talk I will discuss recent work developing discontinuous Galerkin methods for the time-dependent drift--diffusion equation and the coupled Poisson--Nernst--Planck model, which describe the evolution of charged particle concentrations in the presence of a global electric field. The methods in question preserve the positivity (or rather non-negativity) of the charge densities at the Lagrange nodes, and the discretisation of the coupled system uses the natural energy framework to derive stability without any time step restriction. I will also throw in a couple of slides at the end about stable finite element methods for a uniaxially-reduced Oldroyd-B model, as I understand this may be of interest to some in the audience.

Venue: Online
Online Conference Link: https://teams.microsoft.com/meet/36294032529593?p=Q2gB1F6T9uIuFS7hiz