A multilevel discontinuous Galerkin method

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.Received: 5 June 2001, Revised: 12 December 2001, Published online: 4 April 2003Mathematics Subject Classification (1991): 65F10, 65N55, 65N30This research was supported in part by Institute for Mathematics and its Applications, Supercomputing Institute of University of Minnesota, and Deutsche Forschungsgemeinschaft.