Geodesic
On Numerical Methods for the Stokes Problem
Publications de l'Institut de recherche mathématiques de Rennes, Journées éléments finis, no. S4 (1978), article no. 9, 29 p.

Voir la notice de l'acte provenant de la source Numdam

@article{PSMIR_1978___S4_A9_0,
     author = {Glowinski, R. and Pironneau, O.},
     title = {On {Numerical} {Methods} for the {Stokes} {Problem}},
     journal = {Publications de l'Institut de recherche math\'ematiques de Rennes},
     eid = {9},
     pages = {1--29},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S4},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PSMIR_1978___S4_A9_0/}
}
TY  - JOUR
AU  - Glowinski, R.
AU  - Pironneau, O.
TI  - On Numerical Methods for the Stokes Problem
JO  - Publications de l'Institut de recherche mathématiques de Rennes
PY  - 1978
SP  - 1
EP  - 29
IS  - S4
PB  - Département de Mathématiques et Informatique, Université de Rennes
UR  - http://geodesic.mathdoc.fr/item/PSMIR_1978___S4_A9_0/
LA  - en
ID  - PSMIR_1978___S4_A9_0
ER  - 
%0 Journal Article
%A Glowinski, R.
%A Pironneau, O.
%T On Numerical Methods for the Stokes Problem
%J Publications de l'Institut de recherche mathématiques de Rennes
%D 1978
%P 1-29
%N S4
%I Département de Mathématiques et Informatique, Université de Rennes
%U http://geodesic.mathdoc.fr/item/PSMIR_1978___S4_A9_0/
%G en
%F PSMIR_1978___S4_A9_0
Glowinski, R.; Pironneau, O. On Numerical Methods for the Stokes Problem. Publications de l'Institut de recherche mathématiques de Rennes, Journées éléments finis, no. S4 (1978), article  no. 9, 29 p. http://geodesic.mathdoc.fr/item/PSMIR_1978___S4_A9_0/

[1] R. Tenam, Theory and Numerical Analysis of the Navier-Stokes equations, North-Holland, Amsterdam, 1977. | Zbl | MR

[2] R.A. Adams, Sobolev spaces, Academic Press, New York, 1976. | Zbl | MR

[3] J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer-Verlag, New-York, 1972. | Zbl | MR

[4] J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. | Zbl

[5] J.T. Oden, J.N. Reddy, An Introduction to the Mathematical Theory of Finite Elements, John Wiley and Sons, New-York, 1976. | Zbl | MR

[6] R. Glowinski, O. Pironneau, On a mixed finite element approximation for the Stokes problem. (II) Solution of the approximate problems (to appear). | Zbl

[7] O.A. Ladyshenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969. | Zbl | MR

[8] I.S. Duff, N. Munksgaard, H.B. Nielsen, J.K. Reid, Direct solution of sets of linear equations whose matrix is sparse, symmetric and indefinite. Harwell report, C.S.S. Division, A.E.R.E. Harwell, January 1977. | Zbl

[9] C.C. Paige, M.A. Saunders, Solution of sparse indefinite systems of linear equations, SIAM J. Num. Anal., Vol. 12, (1975), pp. 617-629. | Zbl | MR

[10] O. Widlund, A Lanczos method for a class of non-symmetric systems of linear equations (to appear). | Zbl | MR

[11] M. Crouzeix, Etude d'une méthode de linéarisation. Résolution numérique des équations de Stokes stationnaires. Application aux équations de Navier-Stokes stationnaires, in Approximation et méthodes itératives de résolution d'inéquations variationnelles et de problèmes non linéaires, Cahier de l'IRIA N° 12, May 1974, pp. 139-244. | Zbl | MR

[12] M. Fortin, R. Glowinski, Augmented Lagragian in Quadratic Programming, Ch. 1 of Numerical Solution of Boundary Value Problems by Augmented Lagragians, M. Fortin, R. Glowinski Ed., (to appear).

[13] M. Fortin, F. Thomasset, Application to Stokes and Navier-Stokes equations, Ch. 2 of Numerical Solution of Boundary Value Problems by Augmented Lagrangian, M. Fortin, R. Glowinski Ed., (to appear). | MR

[14] J.W. Daniel, The approximate minimization of functionals. Prentice Hall, Englewood Cliffs, 1970. | Zbl | MR

[15] M.R. Hestenes, Multiplier and Gradient Methods, J.O.T.A., 4, N° 5, (1969), pp. 303-320. | Zbl | MR

[16] M.J.D. Powell, A method for non linear optimization in minimization problems, in Optimization, R. Fletcher Ed., Acad. Press, 1969.

[17] R. Glowinski, J.L. Lions, R. Tremolieres, Analyse Numérique des Inéquations Variationnelles, Vol. 1, Dunod-Bordas, Paris, 1976. | Zbl

[18] R. Glowinski, O. Pironneau, Approximation par éléments finis mixtes du problème de Stokes en formulation vitesse-pression. Convergence des solutions approchées. C.R.A.S. Paris, T.286A, 1978, pp. 181-183. | Zbl | MR

[19] R. Glowinski, 0. Pironneau, Approximation par éléments finis mixtes du problème de Stokes en formulation vitesse-pression. Résolution des problèmes approchés. C.R.A.S. Paris, T. 286 A, (1978), pp. 225-228. | Zbl

[20] R. Glowinski, O. Pironneau, Numerical methods for the first biharmonicequation and for the two-dimensional Stokes problem. Comp. Science Dpt., Report STAN-CS-77-615, Stanford University, 1977 and SIAM Review (toappear). | Zbl

[21] R. Glowinski, O. Pironneau, On a mixed finite element approximation for the Stokes problem. (I) Convergence of the approximate solutions (to appear). | Zbl | MR

[22] M.O. Bristeau, R. Glowinski, O. Pironneau, J. Periaux, P. Perier, G. Poirier, Application of Optimal Control Methods to the Calculation of Transonic Flows and Incompressible Viscous Flows, in Numerical Methods in Applied Fluid Dynamics, B. Hunt Ed., Academic Press, London (to appear). | Zbl

[23] C. Taylor, P. Hood, A numerical solution of the Navier-Stokes equations using the finite element technique, Comp. and Fluids, 1, (1973), pp. 73-100. | Zbl | MR

[24] M. Bercovier, O. Pironneau, Estimations d'erreurs pour la résolution du problème de Stokes en éléments finis conformes de Lagrange, C.R.A.S. Paris, T. 285 A, (1977), pp. 1085-1087. | Zbl | MR

[25] J.M. Thomas, Sur l'Analyse Numérique des méthodes d'éléments finis hybrides et mixtes, Thesis, Université Paris VI, 1977.

[26] M. Crouzeix, P.A. Raviart, Conforming and non conforming finite element methods for solving the sationary Stokes equations. R.A.I.R.O., R-3, (1973), pp. 33-76. | Zbl | MR | mathdoc-id

[27] P.A. Raviart, Finite element methods and Navier-Stokes equations. Proceedings of the Third Iria Symposium on Numerical Methods in Engineering and Applied Sciences (to appear). | Zbl | MR

[28] O.C. Zienkiewicz, The Finite Element Method in Engineering Sciences, Mc Graw Hill, 1978. | Zbl | MR

[29] P. Le Tallec, Thesis (to appear).

[30] O. Axelsson, A class of iterative methods for finite element equations, Comp. Methods Applied Mech. Eng., Vol. 9, (1976), N° 2, pp. 123-138. | Zbl | MR

[31] M. Bercovier, Régularisation duale des problèmes variationnels mixtes et extension à quelques problèmes non linéaires, Thesis, Université de Rouen, 1976.

[32] J.H. Argyris, P.C. Dunne, Improved Displacement Finite Element for Incompressible Materials, Chapter 12 of this book. | Zbl

[33] C. Johnson, A mixed finite element method for the Navier-Stokes equations, Research Report 77-IAR, Department of Computer Sciences, Chalmers University of Technology and the University of Goteborg, 1977. | Zbl | MR | mathdoc-id