We develop a framework, which encompasses a large family of conforming and nonconforming numerical schemes, for the approximation of the steady state and transient incompressible Stokes equations with homogeneous Dirichlet's boundary conditions. This framework provides general convergence proofs, by error estimates in the case of the steady problem and by compactness arguments in the case of the transient one. Three classical methods (MAC, Taylor--Hood and Crouzeix-Raviart schemes) are shown to belong to this framework, which also inspires the construction of a novel scheme, whose advantage is to be $H_{\rm div}$ conforming and to retain a small number of degrees of freedom.