Smoothed Aggregation Multigrid for the Discontinuous Galerkin Method

Kurzfassung

The aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems that arise from the discontinuous Galerkin method. The smoothed aggregation multigrid, introduced by Van\v{e}k for the conforming finite element method, is applied to low-order discretizations of convection-diffusion equations. For the elliptic model problem the algorithm is shown to be quasi-optimal. Adjustments for the case of non-vanishing advection, such as directionally implicit smoothing and a suitable splitting of the operator are discussed. Several numerical experiments are presented for two-dimensional problems, including a Newton type linearization of the compressible Navier-Stokes equations.