P. B. Bochev and M. D. Gunzburger, Least-squares finite element methods, Applied Mathematical Sciences, vol.166, 2009.

M. O. Bristeau, O. Pironneau, R. Glowinski, J. Periaux, and P. Perrier, On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods. I. Least square formulations and conjugate gradie, Comput. Methods Appl. Mech. Engrg, vol.17, pp.619-657, 1979.

V. Girault and P. Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, vol.5, 1986.

R. Glowinski, G. Guidoboni, and T. Pan, Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity, J. Comput. Phys, vol.216, issue.1, pp.76-91, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00113341

R. Glowinski, Finite element methods for incompressible viscous flow, vol.9, pp.3-1176, 2003.

R. Glowinski, Variational methods for the numerical solution of nonlinear elliptic problems, CBMS-NSF Regional Conference Series in Applied Mathematics, vol.86, p.3450066, 2015.

W. William, H. Hager, and . Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim, vol.2, issue.1, pp.35-58, 2006.

A. S. Householder, The numerical treatment of a single nonlinear equation, International Series in Pure and Applied Mathematics, 1970.

B. Jiang and L. A. Povinelli, Least-squares finite element method for fluid dynamics, Comput. Methods Appl. Mech. Engrg, vol.81, issue.1, pp.13-37, 1990.

J. Lemoine, A. Munch, and P. Pedregal, Analysis of continuous H ?1-least-squares approaches for the steady Navier-Stokes system

J. Lemoine and A. Münch, A continuous least-squares method for the unsteady Navier-Stokes system: analysis and applications

J. Lions, Quelques méthodes de résolution desprobì emes aux limites non linéaires, Dunod, 1969.

A. Münch, A least-squares formulation for the approximation of controls for the Stokes system, Math. Control Signals Systems, vol.27, issue.1, pp.49-75, 2015.

A. Münch and P. Pedregal, Numerical null controllability of the heat equation through a least squares and variational approach, C. R. Math. Acad. Sci. Paris, vol.351, issue.13-14, pp.277-306, 2013.

A. Quarteroni and A. Valli, Numerical approximation of partial differential equations, Springer Series in Computational Mathematics, vol.23, 1994.

A. Smith and D. Silvester, Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations, IMA J. Numer. Anal, vol.17, issue.4, pp.527-545, 1997.

L. Tartar, An introduction to Navier-Stokes equation and oceanography, Lecture Notes of the Unione Matematica Italiana, vol.1, 2006.

R. Temam, Theory and numerical analysis, 2001.

F. Tone and D. Wirosoetisno, On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations, SIAM J. Numer. Anal, vol.44, issue.1, 2006.