3:00 p.m., Friday (September 8, 2006)
Discontinuous Galerkin methods for incompressible fluid flow
We present and analyze discontinuous Galerkin finite element
methods for the discretization of incompressible fluid flow problems.
The main advantages of these methods in comparison with standard conforming finite element
approaches lie in their robustness in transport-dominated regimes, their local conservation
properties, their flexibility in the mesh-design, and their exact satisfaction
of the incompressibility condition.
We first discuss discontinuous Galerkin for the incompressible
Navier-Stokes equations. The underlying stability mechanisms are
presented, and optimal a-priori error estimates are derived. We then
develop the a-posteriori error estimation of hp-adaptive discretizations.
Finally, we discuss applictions of these results to the numerical approximation of incompressible magneto-hydrodynamics problems that describe electrically conducting incompressible fluids. All our
theoretical results are illustrated and verified in numerical experiments.
Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).