  The numerical approximation of convection-dominated problems continues to
remain subject of strong interest. Families of stabilization techniques for
finite element methods were developed in the past. Adaptive techniques based on
a posteriori error estimates offer potential for further improvements. However,
there is still a lack in robust a posteriori error estimates in natural norms
of the discretizations. Here we combine the dual weighted residual method for
goal-oriented error control with stabilized finite element approximations. By a
duality argument an error representation is derived on that a space-time
adaptive approach is built. It differs from former works on the dual weighted
residual method. Numerical experiments illustrate that our schemes are capable
to resolve layers and sharp fronts with high accuracy and to further reduce
spurious oscillations of approximations.
