Hello,
Answer: the finite element formulation leads to essential boundary conditions which are e.g., in the case of a continuity equation, the quantity of water entered at the boundaries. It is this quantity that is used in the proof of mass conservation and it is this quantity which is entered in the domain. In this sense it is somewhat disconnected from the actual U and V imposed in the momentum equation. Of course these velocities are computed to give the right prescribed discharge, given the local sections involved, but we could be slightly wrong in doing that, without spoiling the mass conservation, only the user could complain that the velocities do not correspond to the actual discharge.
With best regards,
Jean-Michel Hervouet