An Uzawa Domain Decomposition Method for Stokes Problem

Abstract

The Stokes problem plays an important role in computational fluid dynamics since it is encountered in the time discretization of (incompressible) Navier-Stokes equations by operator-splitting methods [2, 3]. Space discretization of the Stokes problem leads to large scale ill-conditioned systems. The Uzawa (preconditioned) conjugate gradient method is an efficient method for solving the Stokes problem. The Uzawa conjugate gradient method is a decomposition coordination method with coordination by a Lagrange multiplier.