[Abstract] We present a mixed finite element method for a class of non-linear Stokes models arising in quasi-Newtonian fluids.
Our results include, as a by-product, a new mixed scheme for the linear Stokes equation. The approach is based on the
introduction of both the flux and the tensor gradient of the velocity as further unknowns, which yields a twofold saddle
point operator equation as the resulting variational formulation. We prove that the continuous and discrete formulations
are well posed, and derive the associated a priori error analysis. The corresponding Galerkin scheme is defined
by using piecewise constant functions and Raviart–Thomas spaces of lowest order
