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.
Mots clés : central discontinuous Galerkin method, discontinuous Galerkin method, linear hyperbolic equation, stability, error estimate
@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: Mod\'elisation math\'ematique et analyse num\'erique}, 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://www.numdam.org/articles/10.1051/m2an:2008018/} }
TY - JOUR AU - Liu, Yingjie AU - Shu, Chi-Wang AU - Tadmor, Eitan AU - Zhang, Mengping TI - $L^2$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 593 EP - 607 VL - 42 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008018/ DO - 10.1051/m2an:2008018 LA - en ID - M2AN_2008__42_4_593_0 ER -
%0 Journal Article %A Liu, Yingjie %A Shu, Chi-Wang %A Tadmor, Eitan %A Zhang, Mengping %T $L^2$ stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 593-607 %V 42 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008018/ %R 10.1051/m2an:2008018 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 4, pp. 593-607. doi : 10.1051/m2an:2008018. http://www.numdam.org/articles/10.1051/m2an:2008018/
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