Mixed finite element analysis of a non-linear three-fields Stokes model

In this article, a mixed finite element analysis of the non-linearStokes problem with monotone constitutive laws is considered.We construct a new three-field model for incompressible fluidswhere the velocity u, the non-linear stress tensor = (|u|)u and the pressure p are the most relevant unknowns. We giveexistence and unicity results for the continuous problem andits approximation. Stable and optimal error estimates underminimal regularity assumptions are derived and numerical resultsare presented. Received 29 April 1999. Accepted 30 November 1999.