In this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, andwe give a detailed analysis of the convergence for different block-relaxation strategies.We find that point-wise block-partitioning gives much better results than the classical cell-wise partitioning.Both for the Baumann-Oden and for the symmetric DG method,with and without interior penalty, the block relaxation methods (Jacobi,Gauss-Seidel and symmetric Gauss-Seidel) give excellent smoothing procedures in a classical multigrid setting.Independent of the mesh size, simple MG cycles give convergence factors 0.075 -- 0.4 per iteration sweep for the different discretisation methods studied.

Iterative methods for linear systems (msc 65F10), Stability and convergence of numerical methods (msc 65N12), Error bounds (msc 65N15), Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65N30), Multigrid methods; domain decomposition (msc 65N55)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Hemker, P.W, Hoffmann, W, & van Raalte, M.H. (2002). Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation. Modelling, Analysis and Simulation [MAS]. CWI.