Numerical analysis of a three-fields model for a quasi-Newtonian flow☆

Abstract We study a finite element approximation of a non-linear three fields version of Stokes' system for incompressible fluids. Such a problem arises when one considers a White-Metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero. The non-linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor. We give existence and unicity results for the continuous problem and its approximation and we prove the error bound.