  The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51
(2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013),
pp.~128--149] for solving incompressible Stokes equations, are extended to
three-dimensional problems. A new analysis of the condition number bound for
using the Dirichlet preconditioner is given. An advantage of this new analysis
is that the numerous coarse level velocity components, required in the previous
analysis to enforce the divergence free subdomain boundary velocity conditions,
are no longer needed. This greatly reduces the size of the coarse level problem
in the algorithm, especially for three-dimensional problems. The coarse level
velocity space can be chosen as simple as for solving scalar elliptic problems
corresponding to each velocity component. Both Dirichlet and lumped
preconditioners are analyzed using a same framework in this new analysis. Their
condition number bounds are proved to be independent of the number of
subdomains for fixed subdomain problem size. Numerical experiments in both two
and three dimensions demonstrate the convergence rate of the algorithms.
