Free Access
Issue
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S279 - S300
DOI https://doi.org/10.1051/m2an/2020038
Published online 26 February 2021
  1. J. Baranger and D. Sandri, Finite element approximation of viscoelastic fluid flow: existence of approximate solutions and error bounds. Numer. Math. 63 (1992) 13–27. [Google Scholar]
  2. G. Barrenechea, E. Castillo and R. Codina, Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilized formulation. IMA J. Numer. Anal. 39 (2019) 792–819. [CrossRef] [Google Scholar]
  3. M.A. Behr, L.P. Franca and T.E. Tezduyar, Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows. Comput. Methods Appl. Mech. Eng. 104 (1993) 31–48. [Google Scholar]
  4. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Science & Business Media (1991). [CrossRef] [Google Scholar]
  5. E. Castillo and R. Codina, Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem. Comput. Methods Appl. Mech. Eng. 279 (2014) 579–605. [Google Scholar]
  6. E. Castillo and R. Codina, Numerical analysis of a stabilized finite element approximation for the three-field linearized viscoelastic fluid problem using arbitrary interpolations. ESAIM: M2AN 51 (2017) 1407–1427. [EDP Sciences] [Google Scholar]
  7. E. Castillo and R. Codina, Finite element approximation of the viscoelastic flow problem: a non-residual based stabilized formulation. Comput. Fluids 142 (2017) 72–78. [Google Scholar]
  8. R. Codina, Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Comput. Methods Appl. Mech. Eng. 190 (2000) 1579–1599. [Google Scholar]
  9. R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales. Comput. Methods Appl. Mech. Eng. 191 (2002) 4295–4321. [Google Scholar]
  10. R. Codina, Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales. Appl. Numer. Math. 58 (2008) 264–283. [Google Scholar]
  11. R. Codina, Finite element approximation of the three-field formulation of the Stokes problem using arbitrary interpolations. SIAM J. Numer. Anal. 47 (2009) 699–718. [Google Scholar]
  12. R. Codina, S. Badia, J. Baiges and J. Principe, Variational multiscale methods in computational fluid dynamics, edited by E. Stein and, R. Borst, T.J.R. Hughes . In: Encyclopedia of Computational Mechanics, John Wiley & Sons Ltd. (2017), 1–28. [Google Scholar]
  13. V.J. Ervin and W.W. Miles, Approximation of time-dependent viscoelastic fluid flow: SUPG approximation. SIAM J. Numer. Anal. 41 (2003) 457–486. [Google Scholar]
  14. R. Fattal and R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor. J. Non-Newtonian Fluid Mech. 123 (2004) 281–285. [CrossRef] [Google Scholar]
  15. R. Fattal and R. Kupferman, Time-dependent simulation of viscoelastic flows at high weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech. 126 (2005) 23–37. [CrossRef] [EDP Sciences] [Google Scholar]
  16. E. Fernández-Cara, F. Guillén and R.R. Ortega, Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind (2002). [Google Scholar]
  17. M. Fortin and R. Pierre, On the convergence of the mixed method of crochet and marchal for viscoelastic flows. Comput. Methods Appl. Mech. Eng. 73 (1989) 341–350. [Google Scholar]
  18. C. Guillopé and J.C. Saut, Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type. ESAIM: M2AN 24 (1990) 369–401. [CrossRef] [EDP Sciences] [Google Scholar]
  19. M. Hieber, Y. Naito and Y. Shibata, Global existence results for Oldroyd-B fluids in exterior domains. J. Differ. Equ. 252 (2012) 2617–2629. [Google Scholar]
  20. T.J.R. Hughes, G.R. Feijóo, L. Mazzei and J. Quincy, The variational multiscale method. A paradigm for computational mechanics. Comput. Methods Appl. Mech. Eng. 166 (1998) 3–24. [Google Scholar]
  21. M.A. Hulsen, A.P.G. Van Heel and B.H.A.A. Van Den Brule, Simulation of viscoelastic flows using Brownian configuration fields. J. Non-Newtonian Fluid Mech. 70 (1997) 79–101. [CrossRef] [Google Scholar]
  22. J. Kwack and A. Masud, A three-field formulation for incompressible viscoelastic fluids. Int. J. Eng. Sci. 48 (2010) 1413–1432. [Google Scholar]
  23. J. Kwack, A. Masud and K.R. Rajagopal, Stabilized mixed three-field formulation for a generalized incompressible Oldroyd-B model. Int. J. Numer. Methods Fluids 83 (2017) 704–734. [Google Scholar]
  24. Y. Kwon, Recent results on the analysis of viscoelastic constitutive equations. Korea-Aust. Rheol. J. 14 (2002) 33–45. [Google Scholar]
  25. A.I. Leonov, Analysis of simple constitutive equations for viscoelastic liquids. J. Non-Newtonian Fluid Mech. 42 (1992) 323–350. [CrossRef] [Google Scholar]
  26. M. Lukáčová-Medvidová, H. Mizerová, B. She and J. Stebel, Error analysis of finite element and finite volume methods for some viscoelastic fluids. J. Numer. Math. 24 (2016) 105–123. [Google Scholar]
  27. J.M. Marchal and M.J. Crochet, A new mixed finite element for calculating viscoelastic flow. J. Non-Newtonian Fluid Mech. 26 (1987) 77–114. [CrossRef] [Google Scholar]
  28. L. Moreno, R. Codina, J. Baiges and E. Castillo, Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation. Comput. Methods Appl. Mech. Eng. 354 (2019) 706–731. [Google Scholar]
  29. R.G. Owens and T.N. Phillips, Computational Rheology. World Scientific 14 (2002). [CrossRef] [Google Scholar]
  30. M. Picasso and J. Rappaz, Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows. ESAIM: M2AN 35 (2001) 879–897. [CrossRef] [EDP Sciences] [Google Scholar]
  31. M. Renardy, Mathematical analysis of viscoelastic flows. Annu. Rev. Fluid Mech. 21 (1989) 21–34. [Google Scholar]
  32. V. Ruas, Une méthode mixte contrainte-déplacement-pression pour la résolution de problemes de viscoélasticité incompressible en déformations planes. C. R. Acad. Sci. Sér. 2: Méc. Phys. Chim. Sci. Univ. Sci. Terre 301 (1985) 1171–1174. [Google Scholar]
  33. P. Saramito, On a modified non-singular log-conformation formulation for Johnson-Segalman viscoelastic fluids. J. Non-Newtonian Fluid Mech. 211 (2014) 16–30. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you