Finite element methods for the three-field Stokes system in ℝ 3 : Galerkin methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 4, pp. 489-525. 
@article{M2AN_1996__30_4_489_0,
     author = {Ruas, V.},
     title = {Finite element methods for the three-field {Stokes} system in $\mathbb {R}^3$ : {Galerkin} methods},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {489--525},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {30},
     number = {4},
     year = {1996},
     mrnumber = {1399501},
     zbl = {0853.76041},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1996__30_4_489_0/}
}
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Ruas, V. Finite element methods for the three-field Stokes system in $\mathbb {R}^3$ : Galerkin methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 4, pp. 489-525. http://www.numdam.org/item/M2AN_1996__30_4_489_0/

[1] G. Acquardro Quacchia, 1987, Resoluçâo Computacional de um Problema de Viscoelasticidade Plana Incompressfvel via Elementos Finitos Mistos, Master's Dissertation. Pontificia Universidade Catolica do Rio de Janieiro.

[2] R. A. Adams, 1970, Sobolev Spaces, Academie Press, New York. | MR | Zbl

[3] D. N. Arnold, F. Brezzi and M. Fortin, 1984, A stable finite element method for the Stokes equation, Calcolo, 21-4, pp. 337-344. | MR | Zbl

[4] G. Astarita and G. Marrucci, 1974, Principles of Non-Newtonian Fluid Mechanics, MGraw-Hill, New York.

[5] I. Babuska, 1973, The finite element method with lagrange multipliers, Numer. Math., 20, pp. 179-192. | MR | Zbl

[6] J. Baranger and D. Sandri, 1991, Approximation par éléments finis d'écoulements de fluides viscoélastiques. Existence de solutions approchées et majorations d'erreur. C. R. Acad. Sci. Paris, 312, Série I, pp. 541-544. | MR | Zbl

[7] R.B. Bird, R. C. Armstrong and O. Hassager, 1987, Dynamics of Polymenc Liquids, Vol. 1, Fluid Mechamcs, Second edition, John Wiley & Sons, New York.

[8] H. Brezzi, 1983, Analyse Fonctionnelle, Théorie et Applications, Masson, Paris. | MR | Zbl

[9] F. Brezzi, 1974, On the existence, uniqueness and approximation of saddlle-point problems arising from lagrange multipliers, RAIRO, Série rouge, Analyse Numérique R-2, pp. 129-151. | Numdam | MR | Zbl

[10] P. G. Ciarlet, 1986, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam. | Zbl

[11] M. J. Crochet, A. R. Davies and K. Walters, 1984, Numencal Simulation of Non-Newtonian Flow, Elsevier, Amsterdam. | Zbl

[12] B. Dupire, 1985, Problemas Varionais Lineares, sua Aproximaçâo e Formulaçöes Mistas, Doctoral Thesis, Pontifïcia Universidade Católica do Rio de Janeiro.

[13] G. Duvaut, 1990, Mécanique des Milieux Continus, Masson, Paris.

[14] G. Duvant and J.-L. Lions, 1972, Les Inéquations en Mécanique et en Physique, Masson, Paris. | Zbl

[15] A. Fortin and M. Fortin, 1990, A preconditioned generalized minimal residual algorithm for the numerical solution of viscoelastic flows, Journal of Non-Newtonian fluid Mechanics, 36, pp. 277-288. | Zbl

[16] M. Fortin and R. Pierre, 1988, On the convergence of the Mixed Method of Crochet & Marchal for Viscoelastic Flows, Comp. Meth. Appl. Mech. Engin., 73, pp. 341-350. | MR | Zbl

[17] L. Franca and R. Stenberg, 1991 Error analysis of some Galerkin-least-squares methods for the elasticity equations, SIAM Journal of Numerical Analysis, 28-6, pp. 1680-1697. | MR | Zbl

[18] P. Germain, 1973, Cours de Mécanique des Milieux Continus, Masson & Cie, Paris. | MR | Zbl

[19] V. Girault and A. P. Raviart, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Serie in Computational Mathematics 5, Springer-Verlag, Berlin. | MR | Zbl

[20] P. Grisvard, 1992, Singularities in Boundary Values Problems, In Research Notes in Applied Mathematics, P. G. Ciarlet & J.-L. Lions eds., Masson & Springer Verlag, Paris. | MR | Zbl

[21] O. Ladyzhenskaya, 1963, The Mathematical Theory of Viscous Incompressible Flow, Gordon & Breach, Reading, Berkshire. | MR | Zbl

[22] P. Lesaint and P. A. Raviart, 1976. On a finite element method for solving the neutron transport equations, in : Mathematical Aspects of Finite Element Methods in Partial Differential Equations, C. de Boor ed., Academic Press, New York. | Zbl

[23] J. L. Lions and E. Magenes, 1968, Problèmes aux Limites Non-homogènes et Applications, Dinod, Paris. | Zbl

[24] M. A. Monteiro Silva Ramos, 1993, Um Modelo Numérico para a Simulaçâo do Escoamento de Fluidos Viscoelâsticos via Elementos Finitos, Doctoral Thesis, Pontificia Univesidade Católica do Rio de Janeiro.

[25] J. Pitkäranta, 1982, On a mixed finite element method for the Stokes Problem in R3, RAIRO, Analyse Numérique, 16-3, pp. 275-291. | Numdam | MR | Zbl

[26] V. Ruas, 1980, Sur l'application de quelques méthodes d'éléments finis à la résolution d'un problème d'élasticité incompressible non linéaire, Rapport de Recherche 24, INRIA, Rocquencourt, France.

[27] V. Ruas, 1982, Une méthode d'éléments finis non conformes en vitesse pour le problème de Stokes tridimensionnel. Matematica Aplicada e Compuracional, 1-1, pp.53-74. | MR | Zbl

[28] V. Ruas, 1985, Une méthode mixte contrainte-déplacement-pression pour la résolution de problèmes de viscoélasticité incompressible en déformations planes, C. R. Acad. Sc., Paris, 301, série II, 16, pp. 1171-1174. | MR | Zbl

[29] V. Ruas, 1985, Finite element solution of 3D viscous flow problems using non standard degrees of freedom, Japan Journal of Applied Mathematics, 2-2, pp. 415-431. | MR | Zbl

[30] V. Ruas and J. H. Carneiro De Araujo, 1992, Un método de elementos finitos quadrilatelares mejorado para el sistema de Stokes asociado al flujo de fluidos viscoelâsticos, Revista Internacional sobre Métodos Numéricos para Càlculo y Diseno en Ingenieria, 8-1, pp.77-85. | MR

[31] V. Ruas, 1992, Finite Element Methods for Three-Dimensional Incompressible Flow, in Finite Element in Fluids, Vol. 8, T. J. Chung ed., Hemisphere Publishing Corporation, Washington, Chapter X, pp. 211-235. | MR

[32] V. Ruas, 1992, A convergent three field quadrilateral finite element method for simulating viscoelastic flow on irregular meshes. Revue Européenne des Éléments finis, 4-1, pp.391-406. | Zbl

[33] V. Ruas, J. H. Carneiro De Araujo, M. A. Silva Ramos, 1993, Approximation of the three-field Stokes System via optimized quadrilateral finite elements, Modélisation Mathématiques et Analyse Numérique, 27-1, pp. 107-127. | Numdam | MR | Zbl

[34] V. Ruas, 1994, An optimal three-field finite element approximation of the Stokes System with continuous extra stresses, Japan Journal of Industrial and Applied Mathematics, 11-1, pp. 103-130. | MR | Zbl

[35] V. Ruas, Galerkin-least-squares finite element methods for the three-field Stokes System in three-dimension space, to appear. | Zbl

[36] D. Sandri, 1993, Analyse d'une formulation à trois champs du problème de Stokes, Modélisation Mathématique et Analyse Numérique, 27-7, pp. 817-841. | Numdam | MR | Zbl

[37] R. I. Tanner, 1985, Engineering Rheology, Claredon Press, Oxford. | MR | Zbl

[38] O. C. Zienkiewicz, 1971, The Finite Element Method in Engineering Science. McGraw Hill, Maidenhead. | MR | Zbl