$L^2$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Liu, Yingjie; Shu, Chi-Wang; Tadmor, Eitan; Zhang, Mengping

doi:10.1051/m2an:2008018

Geodesic

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

Liu, Yingjie ; Shu, Chi-Wang ; Tadmor, Eitan ; Zhang, Mengping

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 593-607

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Résumé

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.

MR Zbl

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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     author = {Liu, Yingjie and Shu, Chi-Wang and Tadmor, Eitan and Zhang, Mengping},
     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 },
     pages = {593--607},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     doi = {10.1051/m2an:2008018},
     mrnumber = {2437775},
     zbl = {1152.65095},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008018/}
}

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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

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