Robust a posteriori error estimates for nonstationary convection-diffusion equations

We consider discretizations of convection dominated nonstationary convection-diffusion equations by A-stable theta-schemes in time and conforming finite elements in space on locally refined, isotropic meshes. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. The error estimates are fully robust in the sense that the ratio between upper and lower bounds is uniformly bounded in time, does not depend on any step-size in space or time nor on any relation between these both, and is uniformly bounded with respect to the size of the convection. Moreover, the estimates are uniform with respect to the size of the zero-order reaction term and also hold for the limit case of vanishing reaction.