Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-27T15:56:50.752Z Has data issue: false hasContentIssue false
  • English
  • Français

Inf-sup conditions for finite-difference approximations of the stokes equations

Published online by Cambridge University Press:  17 February 2009

Dongho Shin  and
John C. Strikwerda
Dongho Shin
Affiliation:
Department of Mathematics, Inje University, Kimhae, Kyungnam 621–749, Korea
John C. Strikwerda
Affiliation:
Department of Computer Sciences and Center for the Mathematical Sciences, University of Wisconsin-Madison, Madison, WI49506, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Inf-sup conditions are proven for three finite-difference approximations of the Stokes equa-tions. The finite-difference approximations use a staggered-mesh scheme and the schemes resulting from the backward and the forward differencings.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 1 , July 1997 , pp. 121 - 134
Copyright
Copyright © Australian Mathematical Society 1997

References

[1] Amsden, A. A. and Harlow, F. H., “The SMAC method: a numerical technique for calculating incompressible fluid flows”, Los Alamos Scientific Laboratory Rept. LA-4370 Los Alamos N. M, (1970).Google Scholar
[2] Aziz, A. K. and Babuška, I., “Survey lectures on the mathematical foundations of the finite element method”, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (ed. Aziz, A. K.) (Academic Press, New York, 1972) 1–362.Google Scholar
[3] Babuška, I., “The finite element method with Lagrangian multipliers”, Numer. Math. 20 (1973) 179–192.CrossRefGoogle Scholar
[4] Brandt, A. and Dinar, N., “Multigrid solutions to elliptic flow problems”, in Numerical Methods for Partial Differential Equations (ed. Parter, S. V.) (Academic Press, New York, 1979) 53–148.CrossRefGoogle Scholar
[5] Brezzi, F., “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers”, R. A. I. R. O., Anal. Numer.R 2 (1974) 129–151.Google Scholar
[6] Girault, V. and Raviart, P. A., Finite Element Methods for Navier-Stokes Equations, Springer series in Computational Mathematics, 5 (Springer, New York, 1986).Google Scholar
[7] Harlow, F. H. and Welch, J. E. “A domain decomposition method for incompressible viscous flow of fluid with free surface”, Phys. Fluids 8 (1965) 2182–2189.CrossRefGoogle Scholar
[8] Patankar, S. V. and Spalding, D. B., “A calculation procedure for heat, mass, and momentum in three dimensional parabolic flows”, Int. J. Heat Mass Trans. 15 (1972) 1787–1806.CrossRefGoogle Scholar
[9] Raithby, G. E. and Schneider, G. D., “Numerical solution of problems in incompressible fluid flow: Treatment of the velocity-pressure coupling”, Num. Heat Trans. 2 (1979) 417–440.Google Scholar
[10] Shin, D., Fast solvers for finite difference approximations for the Stokes and Navier-Stokes equations, Ph. D. Dissertation, Unviersity of Wisconsin at Madison (1992).Google Scholar
[11] Shin, D. H. and Strikwerda, J. C., “Fast solvers for finite difference approximations for the Stokes and Navier-Stokes equations”, to appear.Google Scholar
[12] Shin, D. H. and Strikwerda, J. C., “Convergence estimates for finite difference approximations of the Stokes equations.”, J. Aust. Math. Soc. Sen. B 38 (1996) 274–290.CrossRefGoogle Scholar