[GTP] GTP Seminar at NCAR--James Liu--June 24

[Silvia Gentile]

##Characteristic Methods and Locally Divergence-free Finite Elements##
James Liu
Department of Mathematics
Colorado State University

Tuesday June 24
Foothills Laboratory 2 Room 2133
11:00am (Coffee and tea at 10:45)

This talk is divided into two parts.

Convection-diffusion equations arise from many applications.
Solutions to these problems usually exhibit sharp fronts and
even shocks, which pose serious challenges to existing numerical
methods.  In the first part, we will present the characteristic
methods that efficiently solve convection-diffusion problems.
The characteristic methods can be combined with finite elements
or wavelets to accurately resolve sharp fluid fronts.  Numerical
results of applying the characteristic methods to the kinematics
of two-dimensional resistive magnetohydrodynamic flows will be
presented.

"Divergence-free" is an important physical property that should
be respected by numerical methods.  Locally divergence-free (LDF)
finite elements has gained researchers' attention recently.
In the 2nd part, we examine the approximation properties of the
LDF finite elements and their use in the nonconforming or
discontinuous Galerkin formulations.  Preliminary numerical results
on applying the LDF finite elements to 3-dimensional Maxwell source
problems and eigenvalue problems will be presented.  We will also
discuss applications of the LDF finite elements to the Navier-Stokes
equation.