We are interested in the numerical modeling of the incompressible Navier-Stokes equations, in two dimensions. The adopted approach consists in formulating numerical approximations for an appropriate relaxation model, which formally defines a “singular” hyperbolic perturbation of the incompressible Navier- Stokes equations (such a system can be obtained by a diffusive change of scale from the classical relaxation model associated with the incompressible Euler equations and appears within certain hydrodynamic limits of the Boltzmann equation) The numerical approximation of the relaxation system is then based on a finite element method in space and an implicit-explicit discretization in time, for which we can establish uniform stability properties with respect to the diffusion parameters of the system. In the context of the finite element method, this problem has specific difficulties related to the treatment of the incompressibility condition, while the numerical analysis of the relaxation scheme can be conducted using the techniques which are applied for continuous problems (we refer to the work of Y. Brenier, R. Natalini, A. Klar, L. Pareschi, ...)