AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS

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On 2D elliptic discontinuous Galerkin methods (2006, unknown): “References [10–15]).”
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, background): “This scheme is not symmetric, however it is L(2) stable and convergent, although it has a sub-optimal O(h) order of L(2) errors for even k [8, 66, 107].”
L2 Stability Analysis of the Central Discontinuous Galerkin Method and a Comparison between the Central and Regular Discontinuous Galerkin Methods (2008, methodology): “3 we give an quantitative error estimate for the central DG scheme for polynomial degree up to 1 using Fourier analysis, similar to the technique used in [12,13].”
The discontinuous Galerkin method with Lax-Wendroff type time discretizations (2005, methodology): “[39]), hence the per time stage cost of LWDG and RKDG is the same for such linear cases, thus LWDG is more efficient than RKDG for such linear cases because LWDG is a one step method, see, e.”
Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations (2009, methodology): “This application of the DG method directly to the heat equation with second derivatives could yield a method which behaves nicely in the computation, in the sense that a grid refinement study seems to produce a numerically convergent solution, but is mathematically weakly unstable and has O(1) error”