  Even though substantial progress has been made in the numerical approximation
of convection-dominated problems, its major challenges remain in the scope of
current research. In particular, parameter robust a posteriori error estimates
for quantities of physical interest and adaptive mesh refinement strategies
with proved convergence are still missing. Here, we study numerically the
potential of the Dual Weighted Residual (DWR) approach applied to stabilized
finite element methods to further enhance the quality of approximations. The
impact of a strict application of the DWR methodology is particularly focused
rather than the reduction of computational costs for solving the dual problem
by interpolation or localization.
