Fast time implicit-explicit discontinuous Galerkin method for convection-diffusion flow problems

equations. The time discretization is based on an explicit formulation for the hyperbolic term and an implicit formulation for the parabolic term. The implicit procedure uses a fast iterative algorithm with reduced evaluation cost introduced in [Renac, Marmignon and Coquel, to appear in SIAM J. Sci. Comput.]. The method is here extended to convection dominated ow problems. A second-order discretization in time is achieved by decomposing the integrations of convective and diusive terms with a splitting method. Numerical examples are presented for the linear convection-diusi on equation in one and two space dimensions. The performance of the present method is seen to be improved in terms of CPU time when compared to a full implicit discretization of the parabolic terms in a wide range of Peclet numbers.