DISCONTINUOUS GALERKIN METHOD FOR NONSTATIONARY NONLINEAR CONVECTION-DIFFUSION PROBLEMS: A PRIORI ERROR ESTIMATES

We deal with a numerical solution of a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the interior penalty discontinuous Galerkin methods. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we introduce a priori error estimates in the L-infinity(0, T; L-2(Omega))-norm and in the L-2(0, T; H-1(Omega))-semi-norm. A sketch of the proof and numerical verifications are presented.