  We consider the numerical approximation of the ill-posed data assimilation
problem for stationary convection-diffusion equations and extend our previous
analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated
regime. Slightly adjusting the stabilized finite element method proposed for
dominant diffusion, we draw upon a local error analysis to obtain quasi-optimal
convergence along the characteristics of the convective field through the data
set. The weight function multiplying the discrete solution is taken to be
Lipschitz and a corresponding super approximation result (discrete commutator
property) is proven. The effect of data perturbations is included in the
analysis and we conclude the paper with some numerical experiments.
