Analyse numérique d’une méthode d’éléments finis mixtes vitesse- pression pour le calcul d’écoulements quasi-Newtoniens. (Numerical analysis of a mixed velocity-pressure finite element method for quasi- Newtonian flows). (French) Zbl 0752.76006

Baranger, J.; Najib, K.

Applied mathematics for engineering sciences, Proc. 2nd Fr.-Chil. Symp., Santiago de Chile/Chile 1989, 39-51 (1991).

Summary: [For the entire collection see Zbl 0742.00068.]
We prove abstract error estimates for the approximation of the velocity and the pressure by a mixed FEM for quasi-Newtonian flows whose viscosity obeys the Carreau law with a null second plateau. These estimates can be applied to finite elements used for the solution of Stokes’ problem. In some cases it is convenient to use an \(L^ r\) version of a local inf-sup condition.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76A05	Non-Newtonian fluids
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

error estimates; Carreau law; Stokes’ problem; local inf-sup condition

Citations:

Zbl 0742.00068