no. 1
A new θ-scheme algorithm and incompressible FEM for viscoelastic fluid flows
ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 1, pp. 1-35. 
@article{M2AN_1994__28_1_1_0,
     author = {Saramito, P.},
     title = {A new $\theta $-scheme algorithm and incompressible {FEM} for viscoelastic fluid flows},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1--35},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {28},
     number = {1},
     year = {1994},
     mrnumber = {1259266},
     zbl = {0820.76051},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1994__28_1_1_0/}
}
TY  - JOUR
AU  - Saramito, P.
TI  - A new $\theta $-scheme algorithm and incompressible FEM for viscoelastic fluid flows
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1994
SP  - 1
EP  - 35
VL  - 28
IS  - 1
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1994__28_1_1_0/
LA  - en
ID  - M2AN_1994__28_1_1_0
ER  - 
%0 Journal Article
%A Saramito, P.
%T A new $\theta $-scheme algorithm and incompressible FEM for viscoelastic fluid flows
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1994
%P 1-35
%V 28
%N 1
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1994__28_1_1_0/
%G en
%F M2AN_1994__28_1_1_0
Saramito, P. A new $\theta $-scheme algorithm and incompressible FEM for viscoelastic fluid flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 28 (1994) no. 1, pp. 1-35. http://archive.numdam.org/item/M2AN_1994__28_1_1_0/

[1] R. B. Bird, R. C. Amstrong and O. Hassager, Dynamics of Polymeric Liquid, vol. 1, Fluid Mechanics, 2nd ed. (1987) Wiley, New York.

[2] D. V. Boger, Annu. Rev. Fluid Mech., 19 (1987) 157 : 182.

[3] A. N. Brooks and T. J. R. Hughes, Streamline-Upwind/Petrov-Galerkin Formulation for Convection Dominated Flow with Particular Emphasis on the Incompressible Navier-Stokes Equations, Comp. Meth. in Appl. Mech. and Eng,, 32 (1982) pp. 199-259. | MR | Zbl

[4] M. J. Crochet and J. M. Marchal, A new mixed Finite Element for calculating Viscoelastic Flow, Journal of Non-Newtonian Fluid Mechanics, 26 (1987) pp. 77-114. | Zbl

[5] N. El Kissi, J. M. Piau and B. Tremblay, Low Reynolds number flow visualisation of linear and branched silicones upstream of orifices dies, Journal of Non-Newtonian Fluid Mechanics (1988).

[6] R. E. Evans and K. Walters, Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquid, Journal of Non-Newtonian Fluid Mechanics, 20 (1986) pp. 11-29.

[7] M. Fortin and A. Fortin, A new approach for the FEM simulation of viscoelastic flow, Journal of Non-Newtonian Fluid Mechanics, 32 (1989) pp. 295-310. | Zbl

[8] M. Fortin and R. Glowinski, Lagrangian Augmented Methods, (1981) North Holland.

[9] M. Fortin and R. Pierre, On the convergence of the mixed method of Crochet and Marchal for viscoelastic flow, (1989) Comput. Meth. in Appl. Mech. Eng. | MR | Zbl

[10] V. Girault and P. A. Raviart, Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics, 749, (1979) Springer Verlag. | MR | Zbl

[11] R. Glowinski and J. Périaux, Numerical Methods for Nonlinear Problems in Fluid Dynamics, Proceeding of the International Seminar on Scientific Super-computer, (1987) Feb 2-6. | MR | Zbl

[12] J. B. Goodman and R. J. Leveque, On the accuracy of stable scheme for two dimensional conservation laws, Soc. Ind. Appl. Math. Numer. anal., 25 (1988)pp. 268-284. | MR | Zbl

[13] C. Guillopé and J. C. Saut, Global existence and one-dimensional non-linear stability of shearing motions of viscoelastic fluids of Oldroyd type, Modélisation Mathématique et Analyse Numérique, 24 (1990) pp. 369-401. | Numdam | MR | Zbl

[14] C. Guillopé et J. C. Saut, Résultat d'existence pour les fluides viscoélastiques à loi de comportement de type différentiel, Compte-rendu de l'Académie des Sciences de Paris, 305, série I (1987) pp. 489-492. | MR | Zbl

[15] D. D. Joseph, M. Renardy and J. C. Saut, Hyperbolicity and Change of Type in the Flow of Viscoelastic Fluids, Arch. Ration. Mech. Anal, 87 (1985) pp. 213-251. | MR | Zbl

[16] R. Keunigs, Simulation of Viscoelastic Flow, in Fundamentals of Computer Modeling for Polymer Processing, C. L. Tucker III, Cari Hanser Verlag.

[17] P. Lesaint and P. A. Raviart, On finite element methods for solving the neutron transport equation (1974) Carl de Boor, Academic Press.

[18] X. L. Luo and R. I. Tanner, A Decoupled Finite Element Streamline-Upwind Scheme for Viscoelastic Flow Problems, J. of Non-Newtonian Fluid Mechanics, 31 (1989) pp. 143-162.

[19] J. G. Oldroyd, On the formulation of Rheological equation of states, Proc, Roy. Soc. London, A200 (1950) pp. 523-541. | MR

[20] D. W. Peaceman and H. H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3 (1955) pp. 28-41. | MR | Zbl

[21] M. Renardy, Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations, Z. Angew. Math, u Mech., 65 (1985) pp. 449-451. | MR | Zbl

[22] M. Renardy, Recent advances in the mathematical theory of steady flow of viscoelastic fluids, J. of Non-Newtonian Fluid Mechanics, 9 (1988) pp. 11-24. | Zbl

[23] J. E. Roberts and J. M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis, vol. 3, P. G. Ciarlet and J. L. Lions, North Holland, Amsterdam (Rapport de Recherche 737, INRIA 1987). | MR | Zbl

[24] P. Saramito, Simulation numérique d'écoulements de fluides viscoélastiques par éléments finis incompressibles et une méthode de directions alternées ; applications, thèse de l'INPG (1990) Grenoble.

[25] J. E. Welch, F. H. Harlow, J. P. Shannon and B. J. Daly, The M.A.C. method, LASL report LA3425, Los Alamos Scientific Laboratory, 1965.