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

In this article, a mixed finite element analysis of the non-linear Stokes p roblem with monotone constitutive laws is considered. We construct a new th ree-field model for incompressible fluids where the velocity u, the non-lin ear stress tensor sigma = psi(\delu\)delu and the pressure p are the most r elevant unknowns. We give existence and unicity results for the continuous problem and its approximation. Stable and optimal error estimates under min imal regularity assumptions are derived and numerical results are presented .