ABSTRACT: Using a general approximation setting having the generic properties of finite-elements, we prove uniform boundedness and stability estimates on the discrete Stokes operator in Sobolev spaces with fractional exponents. As a application, we construct approximations for the time-dependent Stokes equations with a source term in $L^p(0,T;\bL^q(\Omega))$ and prove estimates on the discrete pressure and time derivative of the discrete velocity that are similar to those in Sohr and von Wahl [MR847086].