Some implementations of projection methods for Navier-Stokes equations

Jean-Luc Guermond

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 5, page 637-667
  • ISSN: 0764-583X

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Guermond, Jean-Luc. "Some implementations of projection methods for Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.5 (1996): 637-667. <http://eudml.org/doc/193818>.

@article{Guermond1996,
author = {Guermond, Jean-Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {projection step; discretization of boundary conditions; FEM; spectral approximations; preconditioning techniques; Uzawa's operator},
language = {eng},
number = {5},
pages = {637-667},
publisher = {Dunod},
title = {Some implementations of projection methods for Navier-Stokes equations},
url = {http://eudml.org/doc/193818},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Guermond, Jean-Luc
TI - Some implementations of projection methods for Navier-Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 5
SP - 637
EP - 667
LA - eng
KW - projection step; discretization of boundary conditions; FEM; spectral approximations; preconditioning techniques; Uzawa's operator
UR - http://eudml.org/doc/193818
ER -

References

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  1. [1] M. AZAIEZ, C. BERNARDI and M. GRUNDMANN, 1993, Méthodes spectrales pour les équations du milieu poreux, R 93029, Laboratoire d'Analyse Numérique, Paris VI. 
  2. [2] J. B. BELL, P. COLELLA and H. M. GLAZ, 1989, A second order projection method for the incompressible Navier-Stokes equations, J. of Comput. Phys., 85, pp. 257-283. Zbl0681.76030MR1029192
  3. [3] M. BERCOVIER, O. PIRONNEAU, 1979, Error estimates for finite element solution of the Stokes problem in the primitive variables, Numer. Math., 33, pp. 211-224. Zbl0423.65058MR549450
  4. [4] C. BERNARDI, Y. MADAY, 1992, Approximations spectrales des problèmes aux limites elliptiques, Mathématiques et Applications, 10, Springer-Verlag. Zbl0773.47032MR1208043
  5. [5] F. BREZZI, 1974, On the existence uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, R.A.I.R.O., R.2, pp. 129-151. Zbl0338.90047MR365287
  6. [6] J. CAHOUET, J.- P. CHABARD, 1988, Some fast 3-D finite element solvers for generahzed Stokes problem, Int. J. Num. Meth. in Fluids, 8, pp. 269-295. Zbl0665.76038MR953141
  7. [7] C. CANUTO, A. QUARTERONI, 1982, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38, pp. 67-86. Zbl0567.41008MR637287
  8. [8] A. CHORIN, 1968, Numerical simulation of the Navier-Stokes equations, Math. Comp., 22, pp. 745-762. Zbl0198.50103MR242392
  9. [9] J. DONEA, S. GlULIANI, H. LAVAL, L. QUARTAPELLE, 1982, Finite element solution of the unsteady Navier-Stokes equations by a fractional step method, Comput. Meths. Appl. Mech. Engrg., 30, pp. 53-73. Zbl0481.76037
  10. [10] V. GIRAULT and P.-A. RAVIART, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, 5, Springer-Verlag. Zbl0585.65077MR851383
  11. [11] K. GODA, 1979, A multistep technique with implicit difference schemes for calculating two-or three-dimensional cavity flows, J. of Comput. Phys., 30, pp. 76-95. Zbl0405.76017
  12. [12] P. M. GRESHO and S. T. CHAN, 1990, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via finite element method that also introduces a nearly consistent mass matrix. Part I and Part II, Int. J. Numer. Methods Fluids, 11, pp. 587-620. Zbl0712.76035MR1074825
  13. [13] J.- L. GUERMOND, 1994, Sur l'approximation des équations de Navier-Stokes instationnaires par une méthode de projection, C. R. Acad. Sc. Paris, Série I, 319, pp. 887-892. Zbl0813.76066MR1300962
  14. [14] J.-L. GUERMOND, 1994, Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes, Modél. Math. Anal. Numér., 28, 3, pp. 357-374. Zbl0822.65090MR1275349
  15. [15] J.-L. GUERMOND, 1994, Remarques sur les méthodes de projection pour l'approximation des équations de Navier-Stokes, Numer. Math., 67, pp. 465-473. Zbl0802.76057MR1274442
  16. [16] J.- L. GUERMOND and L. QUARTAPELLE, 1995, On the approximation of the unsteady Navier Stokes equations by finite element projection methods, submitted to Numer. Math. and LIMSI reports 95-06, 95-14. Zbl0914.76051MR1645029
  17. [17] G. LABADIE, P. LASBLEIZ, 1983, Quelques méthodes de résolution du problème de Stokes en éléments finis, E. D. F. rapport HE41/83. 01. 
  18. [18] J.-L. LIONS and E. MAGENES, 1968, Problèmes aux limites non homogènes et applications, Dunod, Paris Zbl0165.10801
  19. [19] L. QUARTAPELLE, 1993, Numerical solution of the incompressible Navier-Stokes equations, ISNM 113, Birkhäuser, Basel. Zbl0784.76020MR1266843
  20. [20] R. RANNACHER, 1992, On Chorin's projection method for the incompressible Navier-Stokes equations, Lectures Notes in Mathematics, 1530, Springer, Berlin, pp. 167-183. Zbl0769.76053MR1226515
  21. [21] J. SHEN, 1992, On error estimates of projection methods for Navier-Stokes equations : first-order schemes, SIAM J. Numer. Anal., 29, 1, pp. 57-77. Zbl0741.76051MR1149084
  22. [22] R. TEMAM, 1977, Navier-Stokes Equations, Studies in Mathematics and its Applications, 2, North-Holland. Zbl0383.35057MR609732
  23. [23] R. TEMAM, 1968, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull. Soc. Math. France, 98, pp. 115-152. Zbl0181.18903MR237972
  24. [24] R. TEMAM, 1991, Remark on the pressure boundary condition for the projection method, Theoret. Comput. Fluid Dynamics, 3, pp. 181-184. Zbl0738.76054
  25. [25] J. VAN KAN, 1986, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Stat. Comput., 7, 3, pp. 870-891. Zbl0594.76023MR848569

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