@article{PSMIR_1978___S4_A9_0, author = {Glowinski, R. and Pironneau, O.}, title = {On {Numerical} {Methods} for the {Stokes} {Problem}}, journal = {Publications des s\'eminaires de math\'ematiques et informatique 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://www.numdam.org/item/PSMIR_1978___S4_A9_0/} }
TY - JOUR AU - Glowinski, R. AU - Pironneau, O. TI - On Numerical Methods for the Stokes Problem JO - Publications des séminaires de mathématiques et informatique de Rennes PY - 1978 SP - 1 EP - 29 IS - S4 PB - Département de Mathématiques et Informatique, Université de Rennes UR - http://www.numdam.org/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 des séminaires de mathématiques et informatique de Rennes %D 1978 %P 1-29 %N S4 %I Département de Mathématiques et Informatique, Université de Rennes %U http://www.numdam.org/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 des séminaires de mathématiques et informatique de Rennes, no. S4 (1978), article no. 9, 29 p. http://www.numdam.org/item/PSMIR_1978___S4_A9_0/
[1] Theory and Numerical Analysis of the Navier-Stokes equations, North-Holland, Amsterdam, 1977. | MR | Zbl
,[2] Sobolev spaces, Academic Press, New York, 1976. | MR | Zbl
,[3] Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer-Verlag, New-York, 1972. | MR | Zbl
, ,[4] Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. | Zbl
,[5] An Introduction to the Mathematical Theory of Finite Elements, John Wiley and Sons, New-York, 1976. | MR | Zbl
, ,[6] On a mixed finite element approximation for the Stokes problem. (II) Solution of the approximate problems (to appear). | Zbl
, ,[7] The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969. | MR | Zbl
,[8] 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] Solution of sparse indefinite systems of linear equations, SIAM J. Num. Anal., Vol. 12, (1975), pp. 617-629. | MR | Zbl
, ,[10] A Lanczos method for a class of non-symmetric systems of linear equations (to appear). | MR | Zbl
,[11] 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. | MR | Zbl
, Etude d'une méthode de linéarisation. Résolution numérique des équations de Stokes stationnaires. Application aux équations de Navier-Stokes stationnaires, in[12] 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] 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] The approximate minimization of functionals. Prentice Hall, Englewood Cliffs, 1970. | MR | Zbl
,[15] Multiplier and Gradient Methods, J.O.T.A., 4, N° 5, (1969), pp. 303-320. | MR | Zbl
,[16] A method for non linear optimization in minimization problems, in Optimization, R. Fletcher Ed., Acad. Press, 1969.
,[17] Analyse Numérique des Inéquations Variationnelles, Vol. 1, Dunod-Bordas, Paris, 1976. | Zbl
, , ,[18] 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. | MR | Zbl
, ,[19] 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] 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] On a mixed finite element approximation for the Stokes problem. (I) Convergence of the approximate solutions (to appear). | MR | Zbl
, ,[22] 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] A numerical solution of the Navier-Stokes equations using the finite element technique, Comp. and Fluids, 1, (1973), pp. 73-100. | MR | Zbl
, ,[24] 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. | MR | Zbl
, ,[25] Sur l'Analyse Numérique des méthodes d'éléments finis hybrides et mixtes, Thesis, Université Paris VI, 1977.
,[26] Conforming and non conforming finite element methods for solving the sationary Stokes equations. R.A.I.R.O., R-3, (1973), pp. 33-76. | Numdam | MR | Zbl
, ,[27] Finite element methods and Navier-Stokes equations. Proceedings of the Third Iria Symposium on Numerical Methods in Engineering and Applied Sciences (to appear). | MR | Zbl
,[28] The Finite Element Method in Engineering Sciences, Mc Graw Hill, 1978. | MR | Zbl
,[29] Thesis (to appear).
,[30] A class of iterative methods for finite element equations, Comp. Methods Applied Mech. Eng., Vol. 9, (1976), N° 2, pp. 123-138. | MR | Zbl
,[31] Régularisation duale des problèmes variationnels mixtes et extension à quelques problèmes non linéaires, Thesis, Université de Rouen, 1976.
,[32] Improved Displacement Finite Element for Incompressible Materials, Chapter 12 of this book. | Zbl
, ,[33] 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. | Numdam | MR | Zbl
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