Guido Kanschat reviews several discontinuous Galerkin schemes for elliptic and viscous flow problems. Setting out from Nitsche s method for weak boundary conditions, he studies the interior penalty and LDG methods. Combined with a stable advection discretization, they yield stable DG methods for linear flow problems of Stokes and Oseen type which are applied to the Navier- Stokes problem. The author not only presents the analytical techniques used to study these methods but also devotes a major discussion to the efficient numerical solution of discrete problems.Dr. Guido Kanschat ist Assistant