We study edge-oriented  FEM stabilizations w.r.t.
 linear multigrid solvers and data structures
with the goal to examine the efficiency
of such stabilizations due to the extending matrix stencil which is not
supported
by standard FEM data structures. A new edge-oriented data structure has
been developed to support the additional coupling. So, the local
element-wise
and edge-wise matrices are easily deduced from the global ones. Accordingly,
efficient Vanka smoothers are introduced, namely a full cell-oriented and an
edge-oriented Vanka smoother so that it  becomes possible to
privilege edge-oriented stabilization for CFD
simulations.