M. H. van Raalte

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In this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann–Oden and for the symmetric DG method, we give a detailed analysis of the convergence for celland point-wise block-relaxation strategies. We show that,(More)
In this paper we study the convergence of a multigrid method for the solution of a linear secondorder elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence for di erent block-relaxation strategies. To complement an earlier paper where higher-order methods were studied, here we restrict(More)
In this paper we study a multigrid (MG) method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we give a detailed analysis of the convergence for different block-relaxation strategies. We find that pointwise block-partitioning gives much better results than the classical cellwise(More)
We present the details of the recovery-based DG method for 2-D diffusion problems on unstructured grids. In the recovery approach the diffusive fluxes are based on a smooth, locally recovered solution that in the weak sense is indistinguishable from the discontinuous discrete solution. This eliminates the introduction of ad hoc penalty or coupling terms(More)
In this paper we study the convergence of a multigrid method for the solution of a two-dimensional linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods. For the Baumann-Oden and for the symmetric DG method, we give a detailed analysis of the convergence for celland point-wise block-relaxation strategies. We show that,(More)
Abstract. The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth(More)
In this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we 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(More)
In this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, and we 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(More)