A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow;Sur la résolution numérique des équations de Navier-Stokes pour les écoulements de fluides visqueux incompressibles par réduction à une équation des ondes

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 325, Issue 7, 1997, Pages 783-791

  Dean, Edward J ^a   Glowinski, Roland ^a,b  

^a UNIVERSITY OF HOUSTON   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031256329     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)80060-2     Document Type: Article

References (13)

1. [1] Glowinski R., 1991. Finite element methods for the numerical simulation of incompressible viscous flow. Introduction to the control of the Navier-Stokes equations, in Vortex Dynamics and Vortex Methods, Anderson C. R. and Greengard C. Eds., Lectures in Applied Mathematics, Vol. 28, AMS, Providence, R. I., pp. 219-301.
2. [2] Glowinski R. and Pironneau O., 1992. Finite Element Methods for Navier-Stokes Equations, Annu. Rev. Fluid Mech., 24, pp. 167-204.
3. [3] Beale J. T. and Majda A., 1981. Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp., 37, pp. 243-260.
4. [4] Girault V. and Raviart P. A., 1986. Finite element methods for Navier-Stokes equations, Springer-Verlag, Berlin.
5. [5] Cahouet J. and Chabard J. P., 1988. Some fast 3D solvers for the generalized Stokes problem, Int. J. Num. Meth. Fluids, 8, pp. 269-295.
6. [6] Glowinski R., 1992. Ensuring Well-Posedness by Analogy; Stokes Problem and Boundary Control for the Wave Equation, J. Comput. Phys., 103, 2, pp. 189-221.
7. [7] Brezzi F. and Fortin M., 1991. Mixed and hybrid finite element methods, Springer-Verlag, New York.
8. [8] Ciarlet P. G., 1978. The finite element method for elliptic problems, North-Holland, Amsterdam.
9. [9] Ciarlet P. G., 1991. Basic error estimates for elliptic problems, in Handbook of Numerical Analysis, Vol. II, Ciarlet P. G. and Lions J.-L. Eds., North-Holland, Amsterdam, pp. 17-351.
10. [10] Pironneau O., 1989. Finite element methods for fluids, J. Wiley, Chichester.
11. [11] Lynch D. R. and Gray W. G., 1979. A wave equation model for finite element tidal computations, Comp. and Fluids, 7, pp. 507-534.
12. [12] Chippada S., Dawson C. N., Martinez M. L. and Wheeler M. F., Finite element approximations to the system of shallow water equations, Part I: Continuous time a priori error estimates, SIAM J. Num. Anal. (to appear).
13. [13] Wu J., 1997. Wave equation models to solve multidimensional transport equations, Int. J. Num. Meth. Fluids, 24, 5, pp. 423-439.