Mat-1.600 Laskennallisen tieteen ja
tekniikan seminaari
24.11.2003
14.15
U356
Prof. Dominik Schötzau, UBC
Vancouver
Mixed
Discontinuous Galerkin Methods for Saddle Point Problems
In this talk, we consider mixed discontinuous Galerkin methods for the
discretization of saddle point problems. These are finite element
methods whose approximate solutions are discontinuous across
interelemental boundaries. Discontinuous Galerkin methods are robust in
convection-dominated regimes, ideally suited for hp-adaptivity, and
extremely flexible in the choice of stable element pairings in mixed
approximations.
We first discuss mixed discontinuous Galerkin methods in the context of
incompressible fluid flow problems. The derivation of such methods is
explained for velocity-pressure elements of equal and mixed order. It
is shown that these elements satisfy suitable stability condition
leading to optimal order of convergence. Numerical results demonstrate
that the methods perform well for a wide range of Reynolds numbers. We
then apply similar techniques in the context of the time-harmonic
Maxwell's equations and present a discontinuous Galerkin discretization
of the Maxwell operator in mixed form chosen to provide control on the
divergence of the electric field. Our theoretical and numerical results
indicate that the methods give a promising alternative to standard edge
and face elements.