The author investigates the prospect of using iterative methods for the Stokes problem in the two- and three-dimensional case. More specifically, this paper presents a study of the prospect of utilizing the decomposition of the function space into three subspaces that are orthogonal (as have been introduced by Velte) for the iterative solution of the Stokes equation. The author also proves that Uzawa and Arrow-Hurwitz iterations can proceed fully in the third smallest subspace. For both these methods, optimal iteration parameters are also calculated. For the two-dimensional case, an inclusion of the spectrum of the Schur complement operators of the Stokes problem is provided. The paper also includes a study of the conjugate gradient method in the third Velte subspace, and a convergence estimate is given. Computational illustrations present the efficiency of the proposed approach for discretization, which admits a discrete Velte decomposition. In summary, this is a very interesting paper on discretization methods.