@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {28}, year = {1994}, pages = {1-35}, mrnumber = {1259266}, zbl = {0820.76051}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1994__28_1_1_0} }
Saramito, P. A new $\theta $-scheme algorithm and incompressible FEM for viscoelastic fluid flows. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 1-35. http://gdmltest.u-ga.fr/item/M2AN_1994__28_1_1_0/
[1] Dynamics of Polymeric Liquid, vol. 1, Fluid Mechanics, 2nd ed. (1987) Wiley, New York.
, and ,[2]
, Annu. Rev. Fluid Mech., 19 (1987) 157 : 182.[3] 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 679322 | Zbl 0497.76041
and ,[4] A new mixed Finite Element for calculating Viscoelastic Flow, Journal of Non-Newtonian Fluid Mechanics, 26 (1987) pp. 77-114. | Zbl 0637.76009
and ,[5] Low Reynolds number flow visualisation of linear and branched silicones upstream of orifices dies, Journal of Non-Newtonian Fluid Mechanics (1988).
, and ,[6] 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.
and ,[7] A new approach for the FEM simulation of viscoelastic flow, Journal of Non-Newtonian Fluid Mechanics, 32 (1989) pp. 295-310. | Zbl 0672.76010
and ,[8] Lagrangian Augmented Methods, (1981) North Holland.
and ,[9] On the convergence of the mixed method of Crochet and Marchal for viscoelastic flow, (1989) Comput. Meth. in Appl. Mech. Eng. | MR 1016647 | Zbl 0692.76002
and ,[10] Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics, 749, (1979) Springer Verlag. | MR 548867 | Zbl 0413.65081
and ,[11] Numerical Methods for Nonlinear Problems in Fluid Dynamics, Proceeding of the International Seminar on Scientific Super-computer, (1987) Feb 2-6. | MR 1026941 | Zbl 0666.76080
and ,[12] On the accuracy of stable scheme for two dimensional conservation laws, Soc. Ind. Appl. Math. Numer. anal., 25 (1988)pp. 268-284. | MR 933724 | Zbl 0645.65051
and ,[13] 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 1055305 | Zbl 0701.76011
and ,[14] 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 916317 | Zbl 0624.76008
et ,[15] Hyperbolicity and Change of Type in the Flow of Viscoelastic Fluids, Arch. Ration. Mech. Anal, 87 (1985) pp. 213-251. | MR 768067 | Zbl 0572.76011
, and ,[16] Simulation of Viscoelastic Flow, in Fundamentals of Computer Modeling for Polymer Processing, C. L. Tucker III, Cari Hanser Verlag.
,[17] On finite element methods for solving the neutron transport equation (1974) Carl de Boor, Academic Press.
and ,[18] A Decoupled Finite Element Streamline-Upwind Scheme for Viscoelastic Flow Problems, J. of Non-Newtonian Fluid Mechanics, 31 (1989) pp. 143-162.
and ,[19] On the formulation of Rheological equation of states, Proc, Roy. Soc. London, A200 (1950) pp. 523-541. | MR 35192 | Zbl pre05542443
,[20] The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3 (1955) pp. 28-41. | MR 71874 | Zbl 0067.35801
and ,[21] Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations, Z. Angew. Math, u Mech., 65 (1985) pp. 449-451. | MR 814684 | Zbl 0577.76014
,[22] Recent advances in the mathematical theory of steady flow of viscoelastic fluids, J. of Non-Newtonian Fluid Mechanics, 9 (1988) pp. 11-24. | Zbl 0666.76029
,[23] 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 1115239 | Zbl 0875.65090
and ,[24] 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] The M.A.C. method, LASL report LA3425, Los Alamos Scientific Laboratory, 1965.
, , and ,