Gradient methods for solving Stokes problem

Abstract

In the present paper we consider gradient type iterative methods for solving the Stokes problems in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of meshes for solving two-dimensional problem with a known analytic solution.