On iterative methods for the incompressible Stokes problem

Abstract

In this paper, we discuss various techniques for solving the system of linear equations that arise from the discretization of the incompressible Stokes equations by the finite-element method. The proposed solution methods, based on a suitable approximation of the Schur-complement matrix, are shown to be very effective for a variety of problems. In this paper, we discuss three types of iterative methods. Two of these approaches use the pressure mass matrix as preconditioner (or an approximation) to the Schur complement, whereas the third uses an approximation based on the ideas of least-squares commutators (LSC). We observe that the approximation based on the pressure mass matrix gives h-independent convergence, for both constant and variable viscosity