L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

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The present paper combines two methodologies: The discontinuous Galerkin method and the centered scheme method. The discontinuous Galerkin method has incorporated successful features of finite volume schemes for solving hyperbolic PDEs with shocked solutions. The centered scheme framework is a finite volume / finite difference methodology which avoids explicit Riemann solvers. The analysis provided in this paper indicates that there might be advantages over the traditional discontinuous Galerkin method and the potential to use the difference between the duplicative information over staggered meshes to control numerical dissipation and to possibly guide adaptivity.

David Gottlieb, Associate Editor,
Claude Le Bris and Anthony T. Patera, Editors-in-Chief

L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor and Mengping Zhang
ESAIM: M2AN 42 (2008) 593-607
DOI: http://dx.doi.org/10.1051/m2an:2008018