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linear hyperbolic equation

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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L 2 stability analysis of the central discontinuous Galerkin methodand a comparison between the central and regulardiscontinuous Galerkin methods
Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 42 / Issue 4 / July 2008

Published online by Cambridge University Press:

27 May 2008, pp. 593-607

Print publication:

July 2008
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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 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.