 
Summary: SIAM J. NUMER. ANAL. c 2006 Society for Industrial and Applied Mathematics
Vol. 44, No. 6, pp. 22452269
CFL CONDITION AND BOUNDARY CONDITIONS FOR DGM
APPROXIMATION OF CONVECTIONDIFFUSION
JEANBAPTISTE APOUNG KAMGA AND BRUNO DESPR´ES
Abstract. We propose a general method for the design of discontinuous Galerkin methods
(DGMs) for nonstationary linear equations. The method is based on a particular splitting of the
bilinear forms that appear in the weak DGM. We prove that an appropriate time splitting gives a
stable linear explicit scheme whatever the order of the polynomial approximation. Numerical results
are presented.
Key words. discontinuous Galerkin method, advection diffusion, stability, CFL condition
AMS subject classifications. 65M12, 65M60
DOI. 10.1137/050633159
1. Introduction. The convectiondiffusion equation is widely used in reallife
problems such as contaminant transport in porous media [1, 8, 26]. Due to the ge
ological structure of the problem, the equation is convectiondominant in random
distributed parts of the media. This makes its numerical resolution difficult. While
difference schemes suffer from the complex geometry of the domain, ordinary finite
element methods suffer from their lack of local conservativity [28], and finite volume
methods suffer from their low order of accuracy (due to low order polynomial approx
