, Quadratic velocity/linear pressure Stokes elements, Advances in Computer Methods for Partial Differential Equations, 1992.
, Existence of approximate solutions and error bounds for viscoelastic fluid flow: Characteristics method, Computer Methods in Applied Mechanics and Engineering, vol.148, issue.1-2, pp.39-52, 1997.
DOI : 10.1016/S0045-7825(97)00038-8
, Global solutions to some regularized free-energy-dissipative Oldroyd-like models
, EXISTENCE OF GLOBAL WEAK SOLUTIONS FOR SOME POLYMERIC FLOW MODELS, Mathematical Models and Methods in Applied Sciences, vol.15, issue.06, pp.939-983, 2005.
DOI : 10.1142/S0218202505000625
, Thermodynamics of flowing systems with internal microstructure, 1994.
, GLS and EVSS methods for a three-field Stokes problem arising from viscoelastic flows, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.29-30, pp.3893-3914, 2001.
DOI : 10.1016/S0045-7825(00)00307-8
, Two families of mixed finite elements for second order elliptic problems, Numerische Mathematik, vol.36, issue.2, pp.217-235, 1985.
DOI : 10.1007/BF01389710
, Recent results on mixed finite element methods for second order elliptic problems, Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology, pp.25-43, 1986.
, On the Stabilization of Finite Element Approximations of the Stokes Equations, Efficient Solution of Elliptic System, pp.11-19, 1984.
DOI : 10.1007/978-3-663-14169-3_2
, IntroductionàIntroduction`Introductionà l'analyse numérique matricielle etàet`età l'optimisation, 1985.
, Comparison of some finite element methods for solving the diffusion-convection-reaction equation, Computer Methods in Applied Mechanics and Engineering, vol.156, issue.1-4, pp.185-210, 1998.
DOI : 10.1016/S0045-7825(97)00206-5
, Conforming and non-conforming finite element methods for solving the stationary Stokes equations, RAIRO Anal. Numer, vol.3, pp.33-75, 1973.
, Theory and practice of finite elements, 2004.
DOI : 10.1007/978-1-4757-4355-5
, Global stability of equilibrium manifolds, and ???peaking??? behavior in quadratic differential systems related to viscoelastic models, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.1, pp.30-41, 2007.
DOI : 10.1016/j.jnnfm.2007.03.003
, Constitutive laws for the matrix-logarithm of the conformation tensor, Journal of Non-Newtonian Fluid Mechanics, vol.123, issue.2-3, pp.281-285, 2004.
DOI : 10.1016/j.jnnfm.2004.08.008
, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, Journal of Non-Newtonian Fluid Mechanics, vol.126, issue.1, pp.23-37, 2005.
DOI : 10.1016/j.jnnfm.2004.12.003
, Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind Handbook of numerical analysis Solution of equations in R n (Part 4) Techniques of scientific computing (Part 4) Numerical methods of fluids (Part 2), pp.543-661, 2002.
, Stabilization of Galerkin approximations of transport equations by subgrid modeling, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.6, pp.1293-1316, 1999.
DOI : 10.1051/m2an:1999145
, Existence results for the flow of viscoelastic fluids with a differential constitutive law, Nonlinear Analysis: Theory, Methods & Applications, vol.15, issue.9, pp.849-869, 1990.
DOI : 10.1016/0362-546X(90)90097-Z
, New entropy estimates for the Oldroyd-B model, and related models Available at http://arxiv.org/abs/math, 2007.
, A new finite element formulation for computational fluid dynamics: VII. The stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces, Computer Methods in Applied Mechanics and Engineering, vol.65, issue.1, pp.85-96, 1987.
DOI : 10.1016/0045-7825(87)90184-8
, A sufficient condition for a positive definite configuration tensor in differential models, Journal of Non-Newtonian Fluid Mechanics, vol.38, issue.1, pp.93-100, 1990.
DOI : 10.1016/0377-0257(90)85034-V
, Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms, Journal of Non-Newtonian Fluid Mechanics, vol.127, issue.1, pp.27-39, 2005.
DOI : 10.1016/j.jnnfm.2005.01.002
, Long-time asymptotics of a multiscale model for polymeric fluid flows. Archive for Rational Mechanics and Analysis, pp.97-148, 2006.
, Analysis of locally stabilized mixed finite element methods for the Stokes problem, Mathematics of Computation, vol.58, issue.197, pp.1-10, 1992.
DOI : 10.1090/S0025-5718-1992-1106973-X
, Numerical instability of time-dependent flows, Journal of Non-Newtonian Fluid Mechanics, vol.43, issue.2-3, pp.229-246, 1992.
DOI : 10.1016/0377-0257(92)80026-T
, Simulation of viscoelastic fluid flow, Fundamentals of Computer Modeling for Polymer Processing Hanse, pp.402-470, 1989.
, A survey of computational rheology, Proc. 13th Int. Congr. on Rheology, pp.7-14, 2000.
, A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime, Math. Sci. Preprint available at
, Finite element analysis of planar 4:1 contraction flow with the tensor-logarithmic formulation of differential constitutive equations, Korea-Australia Rheology Journal, vol.16, issue.4, pp.183-191, 2004.
, Stability constraints in the formulation of viscoelastic constitutive equations, Journal of Non-Newtonian Fluid Mechanics, vol.58, issue.1, pp.25-46, 1995.
DOI : 10.1016/0377-0257(94)01341-E
, New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.9-12, pp.1180-1206, 2006.
DOI : 10.1016/j.cma.2005.04.008
, Analysis of simple constitutive equations for viscoelastic liquids. J. non-newton. fluid mech, pp.323-350, 1992.
, On hydrodynamics of viscoelastic fluids, Communications on Pure and Applied Mathematics, vol.39, issue.11, pp.1437-1471, 2005.
DOI : 10.1002/cpa.20074
, GLOBAL SOLUTIONS FOR SOME OLDROYD MODELS OF NON-NEWTONIAN FLOWS, Chinese Annals of Mathematics, vol.21, issue.02, pp.131-146, 2000.
DOI : 10.1142/S0252959900000170
, An energy estimate for the Oldroyd B model: theory and applications, Journal of Non-Newtonian Fluid Mechanics, vol.112, issue.2-3, pp.161-176, 2003.
DOI : 10.1016/S0377-0257(03)00096-X
, Beyond Equilibrium Thermodynamics, 2005.
DOI : 10.1002/0471727903
, On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numerische Mathematik, vol.March, issue.3, pp.309-332, 1982.
DOI : 10.1007/BF01396435
, Non integrable extra stress tensor solution for a flow in a bounded domain of an Oldroyd fluid, Acta Mechanica, vol.58, issue.1-2, pp.95-99, 1999.
DOI : 10.1007/BF01179049
, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, ESAIM: Mathematical Modelling and Numerical Analysis, vol.19, issue.1, pp.111-143, 1985.
DOI : 10.1051/m2an/1985190101111
, Sur l'approximation deséquationsdeséquations de Navier-Stokes, C. R. Acad. Sc. Paris, Série A, vol.262, pp.219-221, 1966.
, Thermodynamics of viscoelastic fluids: The temperature equation, Journal of Rheology, vol.42, issue.5, pp.999-1019, 1998.
DOI : 10.1122/1.550922
, The backward-tracking Lagrangian particle method for transient viscoelastic flows, Journal of Non-Newtonian Fluid Mechanics, vol.91, issue.2-3, pp.273-295, 2000.
DOI : 10.1016/S0377-0257(99)00095-6
, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès
, Alpes : 655, avenue de l'Europe -38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles -BP 93 -06902
, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399