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.