Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem

Pingbing Ming; Zhong-Ci Shi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 5, page 1051-1067
  • ISSN: 0764-583X

How to cite

top

Ming, Pingbing, and Shi, Zhong-Ci. "Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.5 (2000): 1051-1067. <http://eudml.org/doc/194020>.

@article{Ming2000,
author = {Ming, Pingbing, Shi, Zhong-Ci},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {5},
pages = {1051-1067},
publisher = {Dunod},
title = {Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem},
url = {http://eudml.org/doc/194020},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Ming, Pingbing
AU - Shi, Zhong-Ci
TI - Dual combined finite element methods for non-newtonian flow (II). Parameter-dependent problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 5
SP - 1051
EP - 1067
LA - eng
UR - http://eudml.org/doc/194020
ER -

References

top
  1. [1] R.A. Adams, Sobolev Space. Academic Press, New York (1975). Zbl0314.46030MR450957
  2. [2] C. Amrouche and V. Girault, Propriétés fonctionnelles d'opérateurs. Application au problème de stokes en dimension qualconque. Publications du Laboratoire d'Analyse Numérique, No 90025, Université Piere et Marie Curie, Paris, France (1990). 
  3. [3] D.N. Arnold and F. Brezzi, Some new elements for the Reissner-Mindlin plate model, Boundary Value Problems for Partial Differential Equations, edited by C. Baiocchi and J.L. Lions Masson, Paris (1992) 287-292. Zbl0817.73058MR1260452
  4. [4] J. Baranger, K. Najib and D. Sandri, Numerical analysis of a three-field model for a Quasi-Newtonian flow. Comput. Methods Appl. Mech. Engrg. 109 (1993) 281-292. Zbl0844.76004MR1245979
  5. [5] J.W. Barrett and W.B. Liu, Quasi-norm error bounds for the finite element approximation of a Non-Newtonian flow. Numer. Math. 61 (1994) 437-456. Zbl0811.76036MR1301740
  6. [6] F. Brezzi and R.S. Falk, Stability of higher-order Hood-Taylor methods, SIAM J. Numer. Anal. 28 (1991) 581-590. Zbl0731.76042MR1098408
  7. [7] F. Brezzi and M. Fortin, Mixed and Hybrid Methods. Springer-Verlags, New York (1991). Zbl0788.73002MR1115205
  8. [8] P.G. Ciarlet, The Finite Element Method for Elliptic Problem. North Holland, Amsterdam (1978). Zbl0383.65058MR520174
  9. [9] M.J. Crochet, A.R. Davis and K. Walters, Numerical Simulations of Non-Newtonian Flow. Elsevier, Amsterdam, Rheology Series 1 (1984). Zbl0583.76002MR801545
  10. [10] M. Crouzeix and P. Raviart, Conforming and nonconforming finite element methods for solving the stationary stokes equations. RAIRO Anal. Numér. 3 (1973) 33-75. Zbl0302.65087
  11. [11] M. Fortin, Old and new finite elements for incompressible flows. Internat J. Numer. Methods Fluids 1 (1981) 347-364. Zbl0467.76030MR633812
  12. [12] M. Fortin, R. Guénette and R. Pierre, Numerical analysis of the modified EVSS method. Comput. Methods Appl. Mech. Engrg. 143 (1997) 79-95. Zbl0896.76040MR1442390
  13. [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. Zbl0692.76002MR1016647
  14. [14] V. Girault and R.A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer-Verlag, Berlin-New York (1986). Zbl0585.65077MR851383
  15. [15] P. Hood and C. Taylor, A numerical solution of the Navier-Stokes equation using the finite element technique. Comput. and Fluids 1 (1973) 73-100. Zbl0328.76020MR339677
  16. [16] A.F.D. Loula and J.W.C. Guerreiro, Finite element analysis of nonlinear creeping flows. Comput. Methods Appl. Mech. Engrg. 79 (1990) 89-109. Zbl0716.73091MR1044205
  17. [17] J. Malek and S.J. Nečas, Weak and Measure-valued Solution to Evolutionary Partial Differential Equations. Chapman & Hall (1996). Zbl0851.35002
  18. [18] Pingbing Ming and Zhong-ci Shi, Dual combined finite element methods for Non-Newtonian flow (I) Nonlinear Stabilized Methods (1998 Preprint). Zbl1072.76567
  19. [19] Pingbing Ming and Zhong-ci Shi, A technique for the analysis of B-B inequality for non-Newtonian flow (1998 Preprint). MR1807105
  20. [20] D. Sandri, Analyse d'une formulation à trois champs du problème de Stokes. RAIRO Modél. Math. Math. Anal. Numér. 27 (1993) 817-841. Zbl0791.76008MR1249454
  21. [21] D. Sandri, Sur l'approximation numérique des écoulements quasi-newtoniens dont la viscoélastiques suit la Loi Puissance ou le modèle de Carreau. RAIRO-Modèl. Math. Anal. Numér. 27 (1993) 131-155. Zbl0764.76039MR1211613
  22. [22] D. Sandri, A posteriori estimators for mixed finite element approximation of a fluid obeying the power law. Comput. Meths Appl. Mech. Engrg. 166 (1998) 329-340. Zbl0953.76057MR1659179
  23. [23] C. Schwab and M. Suri, Mixed h - p finite element methods for Stokes and non-Newtonian Flow. Research report No 97-19, Seminar für Angewandte Mathematik, ETH Zürich (1997). Zbl0924.76052
  24. [24] B. Szabó and I. Babuška, Finite Element Analysis. John & Sons, Inc. (1991). Zbl0792.73003MR1164869
  25. [25] Tianxiao Zhou, Stabilized finite element methods for a model parameter-dependent problem, in Proc of the Second Conference on Numerical Methods for P.D.E., edited by Longan Ying and Benyu Guo World Scientific, Singapore (1991) 192-194. MR1160831

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.