  We address the issue of designing robust stabilization terms for the
nonconforming virtual element method. To this end, we transfer the problem of
defining the stabilizing bilinear form from the elemental nonconforming virtual
element space, whose functions are not known in closed form, to the dual space
spanned by the known functionals providing the degrees of freedom. By this
approach, we manage to construct different bilinear forms yielding optimal or
quasi-optimal stability bounds and error estimates, under weaker assumptions on
the tessellation than the ones usually considered in this framework. In
particular, we prove optimality under geometrical assumptions allowing a mesh
to have a very large number of arbitrarily small edges per element. Finally, we
numerically assess the performance of the VEM for several different
stabilizations fitting with our new framework on a set of representative test
cases.
