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.
@article{M2AN_2008__42_4_593_0,
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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {42},
year = {2008},
pages = {593-607},
doi = {10.1051/m2an:2008018},
mrnumber = {2437775},
zbl = {1152.65095},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2008__42_4_593_0}
}
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 - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 593-607. doi : 10.1051/m2an:2008018. http://gdmltest.u-ga.fr/item/M2AN_2008__42_4_593_0/
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