L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

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

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 4, page 593-607
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Liu, Yingjie, et al. "L2 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 42.4 (2008): 593-607. <http://eudml.org/doc/250350>.

@article{Liu2008,
abstract = {
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. },
author = {Liu, Yingjie, Shu, Chi-Wang, Tadmor, Eitan, Zhang, Mengping},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Central discontinuous Galerkin method; discontinuous Galerkin method; linear hyperbolic equation; stability; error estimate.; linear hyperbolic equation; central discontinuous Galerkin method; error estimate},
language = {eng},
month = {5},
number = {4},
pages = {593-607},
publisher = {EDP Sciences},
title = {L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods},
url = {http://eudml.org/doc/250350},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Liu, Yingjie
AU - Shu, Chi-Wang
AU - Tadmor, Eitan
AU - Zhang, Mengping
TI - L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/5//
PB - EDP Sciences
VL - 42
IS - 4
SP - 593
EP - 607
AB - 
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.
LA - eng
KW - Central discontinuous Galerkin method; discontinuous Galerkin method; linear hyperbolic equation; stability; error estimate.; linear hyperbolic equation; central discontinuous Galerkin method; error estimate
UR - http://eudml.org/doc/250350
ER -

References

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  10. J. Qiu, B.C. Khoo and C.-W. Shu, A numerical study for the performance of the Runge-Kutta discontinuous Galerkin method based on different numerical fluxes. J. Comput. Phys. 212 (2006) 540–565.  
  11. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys.77 (1988) 439–471.  
  12. M. Zhang and C.-W. Shu, An analysis of three different formulations of the discontinuous Galerkin method for diffusion equations. Math. Models Methods Appl. Sci.13 (2003) 395–413.  
  13. M. Zhang and C.-W. Shu, An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Comput. Fluids34 (2005) 581–592.  

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