Free access
Issue
ESAIM: M2AN
Volume 45, Number 6, November-December 2011
Page(s) 1009 - 1032
DOI http://dx.doi.org/10.1051/m2an/2011007
Published online 10 June 2011
  1. R. Bellman, The stability of solutions of linear differential equations. Duke Math. J. 10 (1943) 643–647. [CrossRef] [MathSciNet]
  2. P. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland (1975).
  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. B. Cockburn, B. Dong, J. Guzman, M. Restelli and R. Sacco, A hybridizable discontinuous Galerkin method for steady-state convection-diffusion-reaction problems. SIAM J. Sci. Comput. 31 (2009) 3827–3846. [CrossRef] [MathSciNet]
  6. 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]
  7. Y.-J. Liu, C.-W. Shu, E. Tadmor and M. Zhang, L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. ESAIM: M2AN 42 (2008) 593–607. [CrossRef] [EDP Sciences]
  8. B. van Leer and S. Nomura, Discontinuous Galerkin for diffusion, in Proceedings of 17th AIAA Computational Fluid Dynamics Conference (2005) 2005–5108.
  9. M. van Raalte and B. van Leer, Bilinear forms for the recovery-based discontinuous Galerkin method for diffusion. Comm. Comput. Phys. 5 (2009) 683–693.
  10. 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]
  11. 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]

Recommended for you