  We present reduced basis approximations and rigorous a posteriori error
bounds for the instationary Stokes equations. We shall discuss both a method
based on the standard formulation as well as a method based on a penalty
approach, which combine techniques developed in our previous work on
parametrized saddle point problems with current reduced basis techniques for
parabolic problems. The analysis then shows how time integration affects the
development of reduced basis a posteriori error bounds as well as the
construction of computationally efficient reduced basis approximation spaces.
To demonstrate their performance in practice, the methods are applied to a
Stokes flow in a two-dimensional microchannel with a parametrized rectangular
obstacle; evolution in time is induced by a time-dependent velocity profile on
the inflow boundary. Numerical results illustrate (i) the rapid convergence of
reduced basis approximations, (ii) the performance of a posteriori error bounds
with respect to sharpness, and (iii) computational efficiency.
