Commun. Comput. Phys., 9 (2011), pp. 1071-1080.


On the Connection Between the Spectral Difference Method and the Discontinuous Galerkin Method

Georg May 1*

1 Aachen Institute for Advanced Study in Computational Engineering Sciences, RWTH Aachen University, Schinkelstr. 2, 52062 Aachen, Germany.

Received 9 February 2010; Accepted (in revised version) 4 June 2010
Available online 10 November 2010
doi:10.4208/cicp.090210.040610a

Abstract

In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin (DG) discretization of a nonlinear conservation law. This allows interpretation of the Spectral Difference Scheme as a particular discretization under the quadrature-free nodal DG paradigm. Moreover, it enables identification of the key differences between the Spectral Difference Scheme and standard nodal DG schemes.

AMS subject classifications: 65N30, 65N99, 65M60, 65M99

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Key words: Spectral difference method, discontinuous Galerkin method, hyperbolic conservation laws, quadrature-free schemes, nodal schemes.

*Corresponding author.
Email: may@aices.rwth-aachen.de (G. May)
 

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