A new nonsymmetric discontinuous Galerkin method for time dependent convection diffusion equations (Q1945376)

The paper describes a nonsymmetric discontinuous Galerkin method for time dependent convection-diffusion equations. The method is introduced with a one-dimensional setting, establishes criteria for nonlinear stability and presents an estimate for the energy norm. Further, the method is extended for two-dimensional diffusion equations. Several numerical examples -- linear heat diffusion, nonlinear convection-diffusion equation, nonlinear reaction-diffusion equation, nonlinear diffusion in porous media and degenerate parabolic equations -- are considered to establish the utility of the method. In all these cases, the numerical errors are well within the bound. The scheme is well suited for parabolic differential equations.