  Non-overlapping domain decomposition methods necessarily have to exchange
Dirichlet and Neumann traces at interfaces in order to be able to converge to
the underlying mono-domain solution. Well known such non-overlapping methods
are the Dirichlet-Neumann method, the FETI and Neumann-Neumann methods, and
optimized Schwarz methods. For all these methods, cross-points in the domain
decomposition configuration where more than two subdomains meet do not pose any
problem at the continuous level, but care must be taken when the methods are
discretized. We show in this paper two possible approaches for the consistent
discretization of Neumann conditions at cross-points in a Finite Element
setting.
