  We have presented a fast method for solving a specific type of block
four-by-four saddlepoint problem arising from the finite element discretization
of the generalized 3D Stokes problem. We analyze the eigenvalue distribution
and the eigenvectors of the preconditioned matrix. Furthermore, we suggested
utilizing the preconditioned global conjugate gradient method (PGCG) as a block
iterative solver for handling multiple right-hand sides within the sub-system
and give some new convergence results. Numerical experiments have shown that
our preconditioned iterative approach is very efficient for solving the 3D
Stokes problem
