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 problem with monotone constitutive laws is considered. We construct a new three-field model for incompressible fluids where the velocity u, the non-linear stress tensor a = Ψ (|⊇u|)⊇u and the pressure p are the most relevant unknowns. We give existence and unicity results for the continuous problem and its approximation. Stable and optimal error estimates under minimal regularity assumptions are derived and numerical results are presented.