A new nonsymmetric discontinuous Galerkin method for time dependent convection diffusion equations
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.
nonsymmetric discontinuous Galerkin method
time dependent convection-diffusion equations
scientific article; zbMATH DE number 6151377