Free access
Issue
ESAIM: M2AN
Volume 35, Number 5, September-October 2001
Page(s) 879 - 897
DOI http://dx.doi.org/10.1051/m2an:2001140
Published online 15 April 2002
  1. F.P.T. Baaijens, Mixed finite element methods for viscoelastic flow analysis: a review. J. Non-Newtonian Fluid Mech. 79 (1998) 361-385. [CrossRef]
  2. I. Babuska, R. Duran, and R. Rodriguez, Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements. SIAM J. Numer. Anal. 29 (1992) 947-964. [CrossRef] [MathSciNet]
  3. J. Baranger and H. El-Amri, Estimateurs a posteriori d'erreur pour le calcul adaptatif d'écoulements quasi-newtoniens. RAIRO Modél. Math. Anal. Numér. 25 (1991) 31-48. [MathSciNet]
  4. J. Baranger and D. Sandri, Finite element approximation of viscoelastic fluid flow. Numer. Math. 63 (1992) 13-27. [CrossRef] [MathSciNet]
  5. M. Behr, L. Franca, and T. Tezduyar, Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows. Comput. Methods Appl. Mech. Engrg. 104 (1993) 31-48. [CrossRef] [MathSciNet]
  6. J. Bonvin, M. Picasso and R. Stenberg, GLS and EVSS methods for a three-field Stokes problem arising from viscoelastic flows. Comput. Methods Appl. Mech. Engrg. 190 (2001) 3893-3914. [CrossRef] [MathSciNet]
  7. J.C. Bonvin, Numerical simulation of viscoelastic fluids with mesoscopic models. Ph.D. thesis, Département de Mathématiques, École Polytechnique Fédérale de Lausanne (2000).
  8. J.C. Bonvin and M. Picasso, Variance reduction methods for CONNFFESSIT-like simulations. J. Non-Newtonian Fluid Mech. 84 (1999) 191-215. [CrossRef]
  9. G. Caloz and J. Rappaz, Numerical analysis for nonlinear and bifurcation problems, in Handbook of Numerical Analysis. Vol. V: Techniques of Scientific Computing (Part 2), P.G. Ciarlet and J.L. Lions, Eds., Elsevier, Amsterdam (1997) 487-637.
  10. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978).
  11. P. Clément, Approximation by finite elements using local regularization. RAIRO Anal. Numér. 8 (1975) 77-84.
  12. M. Fortin, R. Guénette, and R. Pierre, Numerical analysis of the modified EVSS method. Comput. Methods Appl. Mech. Engrg. 143 (1997) 79-95. [CrossRef] [MathSciNet]
  13. M. Fortin and R. Pierre, On the convergence of the mixed method of Crochet and Marchal for viscoelastic flows. Comput. Methods Appl. Mech. Engrg. 73 (1989) 341-350. [CrossRef] [MathSciNet]
  14. L. Franca, S. Frey, and T.J.R. Hughes, Stabilized finite element methods: Application to the advective-diffusive model. Comput. Methods Appl. Mech. Engrg. 95 (1992) 253-276. [CrossRef] [MathSciNet]
  15. L. Franca and R. Stenberg, Error analysis of some GLS methods for elasticity equations. SIAM J. Numer. Anal. 28 (1991) 1680-1697. [CrossRef] [MathSciNet]
  16. X. Gallez, P. Halin, G. Lielens, R. Keunings, and V. Legat, The adaptative Lagrangian particle method for macroscopic and micro-macro computations of time-dependent viscoelastic flows. Comput. Methods Appl. Mech. Engrg. 180 (199) 345-364.
  17. V. Girault and L.R. Scott, Analysis of a 2nd grade-two fluid model with a tangential boundary condition. J. Math. Pures Appl. 78 (1999) 981-1011. [CrossRef] [MathSciNet]
  18. P. Grisvard, Elliptic Problems in Non Smooth Domains. Pitman, Boston (1985).
  19. C. Guillopé and J.-C. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. 15 (1990) 849-869. [CrossRef] [MathSciNet]
  20. M.A. Hulsen, A.P.G. van Heel, and B.H.A.A. van den Brule, Simulation of viscoelastic clows using Brownian configuration Fields. J. Non-Newtonian Fluid Mech. 70 (1997) 79-101. [CrossRef]
  21. K. Najib and D. Sandri, On a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow. Numer. Math. 72 (1995) 223-238. [CrossRef] [MathSciNet]
  22. L.M. Quinzani, R.C. Armstrong, and R.A. Brown, Birefringence and Laser-Doppler velocimetry studies of viscoelastic flow through a planar contraction. J. Non-Newtonian Fluid Mech. 52 (1994) 1-36. [CrossRef]
  23. M. Renardy, Existence of slow steady flows of viscoelastic fluids with differential constitutive equations. Z. Angew. Math. Mech. 65 (1985) 449-451. [CrossRef] [MathSciNet]
  24. V. Ruas, Finite element methods for the three-field stokes system. RAIRO Modél. Math. Anal. Numér. 30 (1996) 489-525. [MathSciNet]
  25. D. Sandri, Analysis of a three-fields approximation of the stokes problem. RAIRO Modél. Math. Anal. Numér. 27 (1993) 817-841. [MathSciNet]
  26. A. Sequeira and M. Baia, A finite element approximation for the steady solution of a second-grade fluid model. J. Comput. Appl. Math. 111 (1999) 281-295. [CrossRef] [MathSciNet]
  27. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis. North-Holland Publishing Company, Amsterdam, New York, Oxford (1984).
  28. R. Verfürth, A posteriori error estimators for the Stokes equations. Numer. Math. 55 (1989) 309-325. [CrossRef] [MathSciNet]

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