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

 Access to full text

 Full (PDF)

 Access to full text

 Full (PDF)

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. Fluids34 (2005) 581–592.  

1. Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang, Central local discontinuous galerkin methods on overlapping cells for diffusion equations
2. Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang, Central local discontinuous galerkin methods on overlapping cells for diffusion equations