In this note we report some basic convergence results for the semi-discrete finite element Galerkin approximation of the nonstationary Navier-Stokes problem. Asymptotic error estimates are established for a wide class of so-called conforming and nonconforming elements as described in the literature for modelling incompressible flows. Since the proofs are lengthy and very technical the present contribution concentrates on a precise statement of the results and only gives some of the key ideas of the argument for proving them. Complete proofs for the case of conforming finite elements may be found in a joint paper of J. Heywood, R. Rautmann and the author [5], whereas the nonconforming case will be treated in detail elsewhere.