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BABUŠKA I., “Error bounds for the finite element method” Numer. Math. 16 (1971), 322–333.
BENAZETH J. C., Thèse de 3ème cycle (to appear).
BERCOVIER M., “Perturbation of mixed variational problems, application to mixed finite element methods” (to appear in RAIRO, Anal. Numer.)
BERCOVIER M., and PIRONNEAU O., “Estimations d'erreurs pour le problème de Stokes en éléments finis de Lagrange”. C.R. Acad. Sci. (to appear).
BORREL M., Etude et mise en oeuvre d'une méthode d'éléments finis de résolution des équations de Navier-Stokes, Thèse de 3e cycle, Paris (1977).
BREZZI F., “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers”, R.A.I.R.O, Serie Anal. Numér. R.2, (1974) 129–151.
BREZZI F. and RAVIART P.A., “Mixed finite element methods for 4 th order elliptic equations”, Topics in Numerical Analysis III (J.J.H. Miller Ed.), Academic Press (to appear).
CIARLET P.G. and GLOWINSKI R., “Dual iterative techniques for solving a finite element approximation of the biharmonic equation“, Comp. Meth. Applied Mech. Eng 5 (1975), 277–295.
CIARLET P.G. and RVIART P.A., “A mixed finite element method for the biharmonic equation”, Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations (C. de Boor, Ed.) Academic Press, N.Y. (1974), 125–145.
CROUZEIX M., “Etude d'une méthode de linéarisation. Résolution numérique des équations de Stokes stationnaires. Application aux equations de Navier-Stokes stationnaires”, Cahiers de 1'I.R.I.A no 12 (Mai 1974).
CROUZEIX M. and RAVIART P.A., “Conforming and nonconforming finite element methods for solving the stationary Stokes equations”, R.A.I.R.O., Serie Anal. Numér., R.3 (1973), 33–75.
FORTIN M., Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la methode des éléments finis, Thèse, Paris (1972).
FORTIN M., “Résolution numérique des équations de Navier-Stokes par des éléments finis de type mixte”, 2nd International Symposium on Finite Element Methods in Flow Problems, S. Margherita Ligure (1976).
GALLAGHER R. H., ODEN J. T., TAYLOR C. and ZIENKIEWICZ O.C. (Editors), Finite Elements in Fluids, Wiley (1975).
GARTLING D.K. and BECKER E.B., “Finite element analysis of viscous incompressible fluid flow I”, Comp. Meth. Applied Mech. Eng. 8 (1976), 51–60.
GIRAULT.V., “A mixed finite element method for the stationary Stokes equations”, SIAM. J. Numer. Anal. (to appear).
GIRAULT V. and RAVIART P.A., “An analysis of mixed finite element methods for the Navier-Stokes equations”(to appear).
GLOWINSKI R., “Approximations externes par éléments finis de Lagrange d'ordre un et deux du problème de Dirichlet pour l'opérateur biharmonique”, Topics in Numerical Analysis (J.J.H. Miller, Ed.), Academic Press, London (1973), 123–171.
GLOWINSKI R. and PIRONNEAU O., “A mixed method for the biharmonic problem”, S.I.A.M. Review (to appear).
JAMET P. and RAVIART P.A., “Numerical solution of the stationary Navier-Stokes equations by finite element methods”, Lecture notes in Computer Science, Springer Verlag, 10 193-223.
LADYZHENSKAYA O.A., “The Mathematical Theory of Viscous Incompressible Flow”, Gordon and Breach, N.Y. (1969).
LESAINT P., “Sur la résolution des systèmes hyperboliques du premier ordre par des méthodes d'éléments finis”, Thèse, Paris (1975).
LESAINT P. and RAVIART P.A., “On a finite element method for solving the neutron transport equation”, Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations (C. de Boor, Ed.), Academic-Press, N.Y. (1974), 89–123.
RAVIART P.A. and THOMAS J.M., “A mixed finite element method for 2nd order elliptic problems”, Lecture notes in Mathematics, Springer Verlag, 606, 292–315.
TAYLOR C. and HOOD P., “A numerical solution of the Navier-Sokes equations using the finite element technique”, Comp. and Fluids 1 (1973), 73–100.
TEMAM R., On the Theory and Numerical Analysis of the Navier-Stokes Equations, North-Holland, Amsterdam (1977).
THOMAS J.M., Sur l'Analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thèse, Paris (1977).
THOMAS SET F., “Numerical solution of the Navier-Stokes equations by finite element methods”, Von Karman Institute for fluid Dynamics, Lecture series 86 (1977).
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Raviart, P.A. (1979). Finite element methods and Navier-Stokes equations. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering, 1977, II. Lecture Notes in Physics, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09119-X_91
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