Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems |
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| Authors: | Emilie Marchandise,Nicolas Chevaugeon,Jean-Franç ois Remacle |
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| Affiliation: | 1. Department of Civil Engineering, Université Catholique de Louvain, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium;2. Center for Systems Engineering and Applied Mechanics (CESAME), Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium;3. Fonds National de la Recherche Scientifique, rue d’Egmont 5, 1000 Bruxelles, Belgium |
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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. |
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| Keywords: | Discontinuous Galerkin method Superconvergence Hyperbolic systems |
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