A new mixed finite element for the Stokes and elasticity problems. (English) Zbl 0777.76051

Farhloul, M.; Fortin, M.

SIAM J. Numer. Anal. 30, No. 4, 971-990 (1993).

Summary: The Stokes problem is approximated by a mixed finite element method using a new finite element, which has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Estimates of optimal order are derived for the errors in the velocity, the pressure, and the gradient of the velocity. This new finite element also works for the elasticity problem, and all estimates are valid uniformly with respect to the compressibility. Finally, some numerical results for the incompressible Navier-Stokes equations are presented.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76D07	Stokes and related (Oseen, etc.) flows
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids
74B05	Classical linear elasticity

Keywords:

error estimates; local conservation of the momentum and the mass