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L 2 stability analysis of the central discontinuous Galerkin methodand a comparison between the central and regulardiscontinuous Galerkin methods

Published online by Cambridge University Press:  27 May 2008

Yingjie Liu ,
Chi-Wang Shu ,
Eitan Tadmor  and
Mengping Zhang
Yingjie Liu
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA. yingjie@math.gatech.edu
Chi-Wang Shu
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. shu@dam.brown.edu .
Eitan Tadmor
Affiliation:
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 .
Mengping Zhang
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China. mpzhang@ustc.edu.cn .
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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 centraldiscontinuous Galerkin method and the regular discontinuousGalerkin method in this context is also made.Numerical experiments are provided to validate the quantitativeconclusions from the analysis.

Keywords

Central discontinuous Galerkin methoddiscontinuous Galerkin methodlinear hyperbolic equationstabilityerror estimate.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 4 , July 2008 , pp. 593 - 607
Copyright
© EDP Sciences, SMAI, 2008

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