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Issue ESAIM: M2AN Volume 42, Number 4, July-August 2008 Page(s) 593 - 607 DOI 10.1051/m2an:2008018 Published online 27 May 2008

ESAIM: M2AN 42 (2008) 593-607
DOI: 10.1051/m2an:2008018

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

Yingjie Liu¹, Chi-Wang Shu², Eitan Tadmor³ and Mengping Zhang<sup>4

1</sup>  School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. yingjie@math.gatech.edu
²  Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. shu@dam.brown.edu .
³  Department of Mathematics, Institute for Physical Science and Technology and Center of Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD 20742, USA. tadmor@cscamm.umd.edu .
⁴  Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. mpzhang@ustc.edu.cn .

Received April 17, 2007. Published online May 27, 2008.

Abstract

We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.

Mathematics Subject Classification. 65M60

Key words: Central discontinuous Galerkin method, discontinuous Galerkin method, linear hyperbolic equation, stability, error estimate.


© EDP Sciences, SMAI 2008

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