In this paper, we present and study a mixed variational method in order to approximate,
with the finite element method, a Stokes problem with Tresca friction boundary conditions.
These non-linear boundary conditions arise in the modeling of mold filling process by
polymer melt, which can slip on a solid wall. The mixed formulation is based on a
dualization of the non-differentiable term which define the slip conditions. Existence and
uniqueness of both continuous and discrete solutions of these problems is guaranteed by
means of continuous and discrete inf-sup conditions that are proved. Velocity and pressure
are approximated by P1 bubble-P1 finite element and piecewise linear
elements are used to discretize the Lagrange multiplier associated to the shear stress on
the friction boundary. Optimal a priori error estimates are derived using
classical tools of finite element analysis and two uncoupled discrete inf-sup conditions
for the pressure and the Lagrange multiplier associated to the fluid shear stress.