Geodesic
L 2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 593-607.

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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.

DOI : 10.1051/m2an:2008018
Classification : 65M60
Keywords: central discontinuous Galerkin method, discontinuous Galerkin method, linear hyperbolic equation, stability, error estimate 
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     title = {$L^2$ stability analysis of the central discontinuous {Galerkin} method and a comparison between the central and regular discontinuous {Galerkin} methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping. $L^2$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 593-607. doi : 10.1051/m2an:2008018. http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008018/

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