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

Mathematical Modelling and Numerical Analysis

Volumn 42, Issue 4, 2008, Pages 593-607

  Liu, Yingjie ^a   Shu, Chi Wang ^b,c   Tadmor, Eitan ^d   Zhang, Mengping ^c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b BROWN UNIVERSITY   (United States)

^c UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^d University of Maryland   (United States)

Author keywords

Central discontinuous Galerkin method; Discontinuous Galerkin method; Error estimate; Linear hyperbolic equation; Stability

Indexed keywords

EID: 46749119923     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008018     Document Type: Article

References (13)

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.
4. B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173-261.
5. S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89-112.
6. G.-S. Jiang and C.-W. Shu, On a cell entropy inequality for discontinuous Galerkin methods. Math. Comput. 62 (1994) 531-538.
7. Y.J. Liu, Central schemes on overlapping cells. J. Comput. Phys. 209 (2005) 82-104.
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.
9. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463.
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. Fluids 34 (2005) 581-592.