Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems

Authors:
Emilie Marchandise;Nicolas Chevaugeon;Jean-François Remacle
Affiliations:
Department of Civil Engineering, Université Catholique de Louvain, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Fonds National de la Recherche Scientifique, rue d'Egmont 5, 1000 Brux ...;Department of Civil Engineering, Université Catholique de Louvain, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium;Department of Civil Engineering, Université Catholique de Louvain, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Center for Systems Engineering and Applied Mechanics (CESAME), Univers ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, we analyze the spatial and spectral superconvergence properties of one-dimensional hyperbolic conservation law by a discontinuous Galerkin (DG) method. The analyses combine classical mathematical arguments with MATLAB experiments. Some properties of the DG schemes are discovered using discrete Fourier analyses: superconvergence of the numerical wave numbers, Radau structure of the X spatial error.