Substructuring preconditioners for the three fields domain decomposition methods

We study a class of preconditioners based on substructuring, for
the discrete Steklov-Poincare operator arising in the three fields formulation of
domain decomposition in two dimensions. Under extremely general assumptions
on the discretization spaces involved, an upper bound is provided on the
condition number of the preconditioned system, which is shown to grow at most
as log(H=h)^2 (H and h denoting, respectively, the diameter and the discretization
mesh-size of the subdomains). Extensive numerical tests performed on
both a plain and a stabilized version of the method confirm the optimality
of such bound.