Higher order semi-implicit discontinuous Galerkin finite element schemes for nonlinear convection-diffusion problems

We deal with the numerical solution of a scalar nonstationary nonlinear convection-diffusion equation. We present a scheme which uses a discontinuous Galerkin finite element method for a space semi-discretization and the resulting system of ordinary differential equations is discretized by backward difference formulae. The linear terms are treated implicitly whereas the nonlinear ones by a higher order explicit extrapolation which preserves the accuracy of the schemes and leads to a system of linear algebraic equations at each time step. Thenumerical examples presented verify expected orders of convergence.