In this talk we shall discuss FEM simulation techniques for vis-
coelastic 
ow with the LCR formulation for which the positive deniteness
of the discrete conformation tensor is guaranteed. The strong coupling be-
tween the velocity gradient and the elastic stress, which leads to a restriction
for the choice of FEM approximation spaces, and the hyperbolic nature of
the problem are handled with EO-FEM. A monolithic Newton multigrid ap-
proach is used to allow a direct steady simulation. We validate quantitatively
this approach for the well-known benchmark of 
ow around cylinder for two
particular models namely Oldroyd-B and Giesekus.