Analysis and application of the IIPG method to quasilinear nonstationary convection–diffusion problems

We develop a numerical method for the solution of convection–diffusion problems with a nonlinear convection and a quasilinear diffusion. We employ the so-called incomplete interior penalty Galerkin (IIPG) method which is suitable for a discretization of quasilinear diffusive terms. We analyse a use of the IIPG technique for a model scalar time-dependent convection–diffusion equation and derive hphp a priori error estimates in the L2L2-norm and the H1H1-seminorm. Moreover, a set of numerical examples verifying the theoretical results is performed. Finally, we present a preliminary application of the IIPG method to the system of the compressible Navier–Stokes equations.