A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations

T. Lu; P. Neittaanmaki; X.-C. Tai

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 6, page 673-708
  • ISSN: 0764-583X

How to cite

top

Lu, T., Neittaanmaki, P., and Tai, X.-C.. "A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.6 (1992): 673-708. <http://eudml.org/doc/193681>.

@article{Lu1992,
author = {Lu, T., Neittaanmaki, P., Tai, X.-C.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {fractional step method; finite element method; splitting-up method; splitting technique; Convergence; linear and nonlinear elliptic problems; quasilinear evolution equations; evolution Navier-Stokes equations},
language = {eng},
number = {6},
pages = {673-708},
publisher = {Dunod},
title = {A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations},
url = {http://eudml.org/doc/193681},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Lu, T.
AU - Neittaanmaki, P.
AU - Tai, X.-C.
TI - A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 6
SP - 673
EP - 708
LA - eng
KW - fractional step method; finite element method; splitting-up method; splitting technique; Convergence; linear and nonlinear elliptic problems; quasilinear evolution equations; evolution Navier-Stokes equations
UR - http://eudml.org/doc/193681
ER -

References

top
  1. [1] A. J. CHORIN, Numerical solution of Navier-Stokes equations Math. Comp., 22 (1968), 745-762. Zbl0198.50103MR242392
  2. [2] C. CUVELIER, A. SEGAL, A. A. VAN STEENHOVEN, Finite element methods and Navier-Stokes equations, D. Reidel Publishing Company, 1986. Zbl0649.65059MR850259
  3. [3] J. DOUGLAS and H. RACHFORD, On the numencal solution of the heat conduction problem in two and three space variables, Trans. Amer. Math. Soc., 82 2 (1956), 421-439. Zbl0070.35401MR84194
  4. [4] G. GiRAULT and P.-A. RAVIART, Finite element methods for Navier-Stokes equations, Theory and algorithms, Springer-Verlag, Berlin, 1986. Zbl0585.65077MR540128
  5. [5] A. R. GOURLAY, Splitting-up methods for time dependent partial differential equations, in The state of the art in numerical analysis (proc. Conf. Univ. York, Heslington, 1976), Academic Press, London, 1977, pp. 757-796. MR451759
  6. [6] J. G. HEYWOOD and R. RANNACHER, Finite element approximation of the nonstationary Navier Stokes problem : I. Regularity of the solution and second-order error estimates for the spatial discretization, SIAM J. Numer. Anal., 19 (1982), 275-311. Zbl0487.76035MR650052
  7. [7] M. KŘIŽEK and P. NEITTAANMÄKI, Finite element approximation to variational problems with applications, Pitman Monographs in Pure and Applied Mathematics 50, Longman, 1990. Zbl0708.65106MR1066462
  8. [8] O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, Second Edition, 1969. Zbl0184.52603MR254401
  9. [9] O. A. LADYZHENSKAYA and V. I. RIVKIND, On the alternating method for the computation of a viscous incompressible fluid flow in cylindrical coordinates, Izv. Akad. Nauk, 35 (1971), 251-268. Zbl0222.76024
  10. [10] J. L. LIONS and R. TEMAM, Éclatement et décentralisation en calcul des variations, in « Proc. of Symposium on Optimization », Lecture Notes in Mathematics, Vol. 132, Springer Verlag, 1970, pp. 196-217. Zbl0223.49033MR467468
  11. [11] T. LU, P. NEITTAANMÄKI and X.-C. TAI, A parallel spliting-up method and its application to Naver-Stokes equations, Appl. Math. Lett., 4 (1989). 25-29. Zbl0718.65066MR1095644
  12. [12] G. I. MARCHUK, Methods of numerical mathematics, Springer-Verlag, 1982. Zbl0485.65003MR661258
  13. [13] D. W. PEACEMAN and H. H. RACHFORD, The numerical solution of parabolic and elliptic differential equations, SIAM, 3 (1955), 28-42. Zbl0067.35801MR71874
  14. [14] J. SHEN, On error estimates of projection methods for Navier-Stokes equations : First order schemes, To appear in SIAM J. Numer. Anal. Zbl0741.76051MR1149084
  15. [15] X. C. TAI and P. NEITTAANMÄKI, A parallel finite element splitting up method for parabolic problems, Numerical methods for partial differential equations, 7 (1991), 209-225. Zbl0747.65084MR1122113
  16. [16] R. TEMAMSur l'approximation de la solution des équations de Navier-Stokes par la méthode de pas fractionnaires (I), Arch. Rational Mech. Anal., 32 (1969), 135-153. Zbl0195.46001MR237973
  17. [17] R. TEMAM, Numerical analysis, D. Reidel Publishing Company, Dordrecht, North-Holland, 1973. Zbl0261.65001MR347099
  18. [18] R. TEMAMNavier-Stokes equations, North-Holland, 1977. Zbl0383.35057MR609732
  19. [19] N. N. YANENKO, The method of fractional steps for solving multi-dimensional problems of mathematical physics, Novosibirsk, Nauka, 1967. Zbl0209.47103
  20. [20] L. YING, Viscosity splitting method for three dimensional Navier-Stokes equations, Acta Math. Sinica New Series, No. 3, 4 (1988), 210-226. Zbl0673.35085MR965569

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.