  We derive computable upper bounds for the difference between an exact
solution of the evolutionary convection-diffusion problem and an approximation
of this solution. The estimates are obtained by certain transformations of the
integral identity that defines the generalized solution. These estimates depend
on neither special properties of the exact solution nor its approximation, and
involve only global constants coming from embedding inequalities. The estimates
are first derived for functions in the corresponding energy space, and then
possible extensions to classes of piecewise continuous approximations are
discussed.
