  In this article we obtain an optimal best approximation type result for fully
discrete approximations of the transient Stokes problem. For the time
discretization we use the discontinuous Galerkin method and for the spatial
discretization we use standard finite elements for the Stokes problem
satisfying the discrete inf-sup condition. The analysis uses the technique of
discrete maximal parabolic regularity. The results require only natural
assumptions on the data and do not assume any additional smoothness of the
solutions.
