  The efficient and reliable approximation of convection-dominated problems
continues to remain a challenging task. To overcome the difficulties associated
with the discretization of convection-dominated equations, stabilization
techniques and a posteriori error control mechanisms with mesh adaptivity were
developed and studied in the past. Nevertheless, the derivation of robust a
posteriori error estimates for standard quantities and in computable norms is
still an unresolved problem and under investigation. Here we combine the Dual
Weighted Residual (DWR) method for goal-oriented error control with stabilized
finite element methods. By a duality argument an error representation is
derived on that an adaptive strategy is built. The key ingredient of this work
is the application of a higher order discretization of the dual problem in
order to make a robust error control for user-chosen quantities of interest
feasible. By numerical experiments in 2D and 3D we illustrate that this
interpretation of the DWR methodology is capable to resolve layers and sharp
fronts with high accuracy and to further reduce spurious oscillations.
