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All issues Volume 56 / No 3 (May-June 2022) ESAIM: M2AN, 56 3 (2022) 1007-1025 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 3, May-June 2022
Page(s) 1007 - 1025
DOI https://doi.org/10.1051/m2an/2022024
Published online 25 April 2022
  1. N. Arada, P. Correia and A. Sequeira, Analysis and finite element simulations of a second-order fluid model in a bounded domain. Numer. Methods Part. Differ. Equ. Int. J. 23 (2007) 1468–1500. [CrossRef] [Google Scholar]
  2. H.A. Barnes, J.F. Hutton and K. Walters, An Introduction to Rheology. Vol. 3. Elsevier (1989). [Google Scholar]
  3. J.-M. Bernard, Solutions globales variationnelles et classiques des fluides de grade deux. C. R. Acad. Sci. Ser. I Math. 327 (1998) 953–958. [Google Scholar]
  4. J.-M. Bernard, Stationary problem of second-grade fluids in three dimensions: existence, uniqueness and regularity. Math. Methods Appl. Sci. 22 (1999) 655–687. [CrossRef] [MathSciNet] [Google Scholar]
  5. J.-M. Bernard, Problem of second grade fluids in convex polyhedrons. SIAM J. Math. Anal. 44 (2012) 2018–2038. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.-M. Bernard, Steady transport equation in the case where the normal component of the velocity does not vanish on the boundary. SIAM J. Math. Anal. 44 (2012) 993–1018. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-M. Bernard, Solutions in H1 of the steady transport equation in a bounded polygon with a full non-homogeneous velocity. J. Math. Pures App. 107 (2017) 697–736. [CrossRef] [Google Scholar]
  8. J.-M. Bernard, Fully nonhomogeneous problem of two-dimensional second grade fluids. Math. Methods Appl. Sci. 41 (2018) 6772–6792. [CrossRef] [MathSciNet] [Google Scholar]
  9. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. 3rd edition. Springer-Verlag (2008). [Google Scholar]
  10. D. Cioranescu, V. Girault and K.R. Rajagopal, Mechanics and Mathematics of Fluids of the Differential Type. In Vol. 35 of Advances in Mechanics and Mathematics. Springer (2016). [CrossRef] [Google Scholar]
  11. J.L. Ericksen and R.S. Rivlin, Stress-deformation relations for isotropic materials. Arch. Ration. Mech. Anal. 4 (1955) 323–425. [Google Scholar]
  12. B.A. Gecim, Non-Newtonian effects of multigrade oils on journal bearing performance. Tribol. Trans. 33 (1990) 384–394. [CrossRef] [Google Scholar]
  13. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer Verlag, Berlin (1986). [CrossRef] [Google Scholar]
  14. V. Girault and L.R. Scott, Finite element discretizations of a two-dimensional grade-two fluid model. ESAIM: M2AN 35 (2001) 1007–1053. [CrossRef] [EDP Sciences] [Google Scholar]
  15. V. Girault and L.R. Scott, Analysis of a two-dimensional grade-two fluid model with a tangential boundary condition. J. Math. Pures Appl. 78 (1999) 981–1011. [CrossRef] [MathSciNet] [Google Scholar]
  16. V. Girault and L.R. Scott, Wellposedness of some Oldroyd models that lack explicit dissipation. Research Report UC/CS TR-2017-04, Dept. Comp. Sci., Univ. Chicago (2017). [Google Scholar]
  17. D. Gómez-Díaz and J.M. Navaza, Rheology of aqueous solutions of food additives: effect of concentration, temperature and blending. J. Food Eng. 56 (2003) 387–392. [CrossRef] [Google Scholar]
  18. L.D. Landau and E.M. Lifshitz, Fluid Mechanics. Pergamon Press (1959). [Google Scholar]
  19. R. Lapasin, Rheology of Industrial Polysaccharides: Theory and Applications. Springer Science & Business Media (2012). [Google Scholar]
  20. A.S. Lodge, Low-shear-rate rheometry and polymer quality control. Chem. Eng. Commun. 32 (1985) 1–60. [CrossRef] [Google Scholar]
  21. A.S. Lodge, W.G. Pritchard and L.R. Scott, The hole–pressure problem. IMA J. Appl. Math. 46 (1991) 39–66. [CrossRef] [MathSciNet] [Google Scholar]
  22. H. Morgan and L. Ridgway Scott, Towards a unified finite element method for the Stokes equations. SIAM J. Sci. Comput. 40 (2018) A130–A141. [CrossRef] [Google Scholar]
  23. M. Nyström, H.R. Tamaddon Jahromi, M. Stading and M.F. Webster, Hyperbolic contraction measuring systems for extensional flow. Mech. Time-Depend. Mater. 21 (2017) 455–479. [CrossRef] [Google Scholar]
  24. S. Pollock and L. Ridgway Scott, Transport equations with inflow boundary conditions. Submitted (2022). [Google Scholar]
  25. L. Schwartz, Théorie des Distributions. Hermann, Paris (1966). [Google Scholar]
  26. L.R. Scott, C1 piecewise polynomials satisfying boundary conditions. Research Report UC/CS TR-2019-18, Dept. Comp. Sci., Univ. Chicago (2019). [Google Scholar]
  27. T.W. Selby, The non-Newtonian characteristics of lubricating oils. ASLE Trans. 1 (1958) 68–81. [CrossRef] [Google Scholar]
  28. P.A. Vasquez, Y. Jin, E. Palmer, D. Hill and M. Gregory Forest, Modeling and simulation of mucus flow in human bronchial epithelial cell cultures – Part I: idealized axisymmetric swirling flow. PLoS Comput. Biol. 12 (2016) 1–28. [Google Scholar]

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