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ESAIM: M2AN
Volume 42, Number 4, July-August 2008
Page(s) 593 - 607
DOI http://dx.doi.org/10.1051/m2an:2008018
Published online 27 May 2008
  1. P. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland (1975).
  2. B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52 (1989) 411–435.
  3. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440–2463. [CrossRef] [MathSciNet]
  4. B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173–261. [CrossRef] [MathSciNet]
  5. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112. [NASA ADS] [CrossRef] [MathSciNet]
  6. G.-S. Jiang and C.-W. Shu, On a cell entropy inequality for discontinuous Galerkin methods. Math. Comput. 62 (1994) 531–538. [CrossRef] [MathSciNet]
  7. Y.J. Liu, Central schemes on overlapping cells. J. Comput. Phys. 209 (2005) 82–104. [CrossRef] [MathSciNet]
  8. Y.J. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction. SIAM J. Numer. Anal. 45 (2007) 2442–2467. [CrossRef] [MathSciNet]
  9. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [CrossRef] [MathSciNet]
  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. [NASA ADS] [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  13. M. Zhang and C.-W. Shu, An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Comput. Fluids 34 (2005) 581–592. [CrossRef]

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