Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems

Emilie Marchandise (1) , Nicolas Chevaugeon (1) , Jean-François Remacle (1)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain

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.

Mots clés: Discontinuous Galerkin method; Superconvergence; Hyperbolic systems

Domaines: Mécanique [physics.med-ph]; Matériaux

Emilie Marchandise, Nicolas Chevaugeon, Jean-François Remacle. Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems. Journal of Computational and Applied Mathematics, 2008, 215 (2), pp.484-494. ⟨10.1016/j.cam.2006.03.061⟩. ⟨hal-01007314⟩