AbstractWe consider first and second‐order implicit time stepping procedures for the non‐stationary Stokes equations in bounded domains of ℝ3. Using energy estimates we prove the optimal convergence properties in the Sobolev spacesHm(G)(m = 0, 1, 2) uniformly in time, provided that the Stokes solution has a certain degree of regularity. Here in the case of the second‐order scheme (method of Crank–Nicholson) the Stokes solution has to satisfy a non‐local compatibility condition at the initial timet= O, which can be satisfied by a special initial c