This paper presents the common mathematical features which are leading to convergence properties for a family of numerical schemes applied to the discretisation of the steady and transient incompressible Navier-Stokes equations with homogeneous Dirichlet’s boundary conditions. This family includes the Taylor-Hood scheme, the MAC scheme, the Crouzeix-Raviart scheme generalized into the Hybrid Mixed Mimetic scheme, which can be combined with a variety of discretisations for the nonlinear convection term, each of them being more efficient than the others in particular situa- tions. We provide tools for analyzing all the combined methods, and proving their convergence to a weak solution of the problem.