Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems

Marchandise, Emilie;Chevaugeon, Nicolas;Remacle, Jean-François
(2008) 3rd International Conference on Advanced Computational Methods in Engineering — Location: Ghent(Belgium) (30.May.2005)

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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. (C) 2007 Elsevier B.V. All rights reserved.
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Marchandise, E., Chevaugeon, N., & Remacle, J.-F. (2008). Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems. Journal of Computational and Applied Mathematics, 215(2), 484-494. https://doi.org/10.1016/j.cam.2006.03.061 (Original work published 2008)