Discontinuous Galerkin method for convection-diffusion problems

Jiri Hozman, Vit Dolejsi

A wide class of problems of fluid mechanics is governed by
the combined effects of convection and diffusion. The first part of
this contribution is concerned with an analysis of error estimates of
the discontinuous Galerkin finite element method (DGFEM) applied to
the space semidiscretization of a nonstationary two-dimensional convection-diffusion
equation with nonlinear convection and nonlinear diffusion. The attention
is paid to the derivation of the error estimates for three variants
of DGFEM, namely NIPG, SIPG and IIPG types of stabilizations of diffusion
terms. The second part presents a set of numerical examples verifying
the theoretical results, namely applications of NIPG, SIPG and IIPG
methods to the system of compressible Navier-Stokes equations, where
these techniques are applied to a steady flow around the NACA0012 profile
and the error of DGFEM is treated with respect to the coefficients of
drag and lift.