SECOND ORDER TIME DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR CONVECTION-DIFFUSION PROBLEMS

We deal with a numerical solution of a scalar nonstationary convection-diffusion equation with a nonlinear convection and a linear diffusion. We carry out the space semi-discretization with the aid of the nonsymmetric interior penalty Galerkin (NIPG) method and the time discretization by the time discontinuous Galerkin method linearized by extrapolation from previous time interval. The resulting scheme is unconditionally stable, has a high order of accuracy with respect to space and time coordinates and requires only solutions of linear algebraic problems at each time step. We derive a priori error estimate in the L-2-norm.