Résumé
The gradient schemes framework encompasses several conforming and nonconforming numerical schemes for diffusion equations. We develop here this framework for the approximation of the steady-state and transient incompressible Stokes equations with homogeneous Dirichlet boundary conditions. Using this framework, we establish generic convergence results-by error estimates in the case of the steady problem, and by compactness arguments in the case of the transient problem-that are applicable to both old and new schemes for Stokes' equations. Three classical methods (MAC, Taylor-Hood and Crouzeix-Raviart schemes) are shown to fit into the gradient schemes framework; some of the convergence results obtained for those through the framework are new. We also show that a Hybrid Mimetic Mixed scheme, extension of the Crouzeix-Raviart scheme to a very general polyhedral mesh, can be designed within the gradient schemes framework; this scheme is new for Stokes' equations, and our abstract analysis establishes its convergence along with error estimates.