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.

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Modelling, Analysis and Simulation [MAS]
Scientific Computing

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