  This work presents a numerical investigation of different approximation
techniques for the temporal weights used in the Dual Weighted Residual (DWR)
method applied to a time-dependent convection-diffusion equation which is
assumed to be convection-dominated. It is a continuation of a previous work by
the authors where spatial weights were compared for a steady-state case. A
higher-order finite elements approach is compared to a more cost-efficient
higher-order reconstruction approach. Numerical examples point out the results
regarding accuracy, efficiency and stability reasons.
