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Vorticity-velocity formulation for the stationary Navier-Stokes equations: the three-dimensional case. (English) Zbl 0827.76016

Summary: We propose a mixed method for the vorticity-velocity formulation of the stationary Stokes and Navier-Stokes equations in three space dimensions, the unknowns being the vorticity and the velocity of the fluid.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows

Keywords:

mixed method
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References:

[1] Quartappelle, L., Numerical Solutions of the Navier-Stokes Equations (1993), Birkhäuser: Birkhäuser Berlin · Zbl 0784.76020
[2] Girault, V.; Raviart, R. A., Finite Element Method for Navier-Stokes Equations. Theory and Algorithms (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0396.65070
[3] Daube, Resolution of the 2D N.S. equation in velocity-vorticity form by means of an influence matrice technique, J. Comput. Phys., 103, 402-414 (1992) · Zbl 0763.76046
[4] Temam, R., Navier-Stokes Equations. Theory and Numerical Analysis (1979), North-Holland: North-Holland Amsterdam · Zbl 0426.35003
[5] T. Tachim Medjo, Vorticity-velocity formulation for the stationary Navier-Stokes equations: The three-dimensional case (to appear).; T. Tachim Medjo, Vorticity-velocity formulation for the stationary Navier-Stokes equations: The three-dimensional case (to appear). · Zbl 0827.76016
[6] T. Tachim Medjo, The Navier-Stokes equations in the vorticity-velocity formulation: The two dimensional case (to appear).; T. Tachim Medjo, The Navier-Stokes equations in the vorticity-velocity formulation: The two dimensional case (to appear). · Zbl 0858.76018
[7] Temam, R., Navier-Stokes equations and functional analysis, (CBMS-NSF Regional Conference Series in Applied Mathematics (1983), SIAM: SIAM Philadelphia) · Zbl 0438.76027
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