Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale

Jean-Luc Guermond

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 1, page 169-189
  • ISSN: 0764-583X

How to cite

top

Guermond, Jean-Luc. "Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.1 (1999): 169-189. <http://eudml.org/doc/193909>.

@article{Guermond1999,
author = {Guermond, Jean-Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error estimation; fractional step; Chorin-Temam projection method; three-level backward finite difference; Galerkin technique; splitting error},
language = {fre},
number = {1},
pages = {169-189},
publisher = {Dunod},
title = {Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale},
url = {http://eudml.org/doc/193909},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Guermond, Jean-Luc
TI - Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 1
SP - 169
EP - 189
LA - fre
KW - error estimation; fractional step; Chorin-Temam projection method; three-level backward finite difference; Galerkin technique; splitting error
UR - http://eudml.org/doc/193909
ER -

References

top
  1. [1] C. Amrouche and V. Girault, On the existence and regularity of the solution of Stokes problem in arbitrary dimension. Proc. Japan Acad. 67 (1991) 171-175. Zbl0752.35047MR1114965
  2. [2] I. Babŭska, The finite element method with Lagragian multipliers. Numer. Math. 20 (1973) 179-192. Zbl0258.65108MR359352
  3. [3] C. Bernardi and G. Raugel, A conforming finite element method for the time-dependent Navier-Stokes equations. SIAM J. Numer. Anal. 22 (1985) 455-473. Zbl0578.65122MR787570
  4. [4] H. Brezis, Analyse fonctionnelle, théorie et applications. Masson, Paris (1983). Zbl0511.46001MR697382
  5. [5] F. Brezzi, On the existence uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. RAIRO R2 (1974) 129-151. Zbl0338.90047MR365287
  6. [6] L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova 31 (1961) 308-340. Zbl0116.18002MR138894
  7. [7] A.J. Chorin, Numerical solution of the Navier-Stokes equations Math. Comp 22 (1968) 745-762. Zbl0198.50103MR242392
  8. [8] A. J. Chorin, On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comp. 23 (1969) 341-353. Zbl0184.20103MR242393
  9. [9] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer Series in Computational Mathematics 5 Springer-Verlag (1986). Zbl0585.65077MR851383
  10. [10] K. Goda, A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows J.Comput. Phys. 30 (1979) 76-95. Zbl0405.76017
  11. [11] J.-L. Guermond, Some practical implementations of projection methods for Navier-Stokes equations. RAIRO Modél. Math.Anal. Numér. 30 (1996) 637-667. Zbl0861.76065MR1411394
  12. [12] J.-L. Guermond, Sur l'approximation des équations de Navier-Stokes instationnaires par une méthode de projection. C. R.Acad. Sci. Paris 319 (1994) 887-892. Zbl0813.76066MR1300962
  13. [13] J.-L. Guermond and L. Quartapelle, Unconditionally stable Finite-Element Method for the unsteady Navier-Stokes equations, 9th International Conference on Finite Element in Fluids. Venezia, Italy, October 1995 I 367-376. 
  14. [14] J.-L. Guermond and L. Quartapelle, Calculation of incompressible viscous flows by an unconditionally stable projection finite element method. J. Comput. Phys. 132 (1997) 12-33. Zbl0879.76050MR1440332
  15. [15] J.-L. Guermond and L. Quartapelle, On the approximation of the Navier-Stokes equations by finite element projection methods Numer. Math. 80 (1998) 207-238. Zbl0914.76051MR1645029
  16. [16] J.G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier-Stokes problem, I, II, III, and IV. SIAM J. Numer. Anal. 19 (1982) 275-311, 23 (1986) 750-777; 25 (1988) 489-512, 27 (1990) 353-384. Zbl0611.76036
  17. [17] L. Quartapelle, Numerical Solution of the Incompressible Navier-Stokes Equations, ISNM 113 Birkhâuser, Basel (1993). Zbl0784.76020MR1266843
  18. [18] A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer Series in Computational Mathematics, Vol. 5, Springer-Verlag (1994). Zbl0803.65088MR1299729
  19. [19] R. Rannacher, On Chorin's projection method for the incompressible Navier-Stokes equations. Lectures Notes in MathematicsSpringer, Berlin (1992) 167-183. Zbl0769.76053MR1226515
  20. [20] R. Temam, Navier-Stokes Equations. Studies in Mathematics and its Applications, Vol 2. North-Holland (1977). Zbl0383.35057MR609732
  21. [21] R. Temam, Une méthode d'approximation de la solution des équations de Navier-Stokes. Bull. Soc. Math. France 98 (1968)115-152. Zbl0181.18903MR237972
  22. [22] J. Van Kan, A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7 (1986) 870-891. Zbl0594.76023MR848569

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.