Inexact Uzawa Algorithms for Nonsymmetric Saddle Point
Problems

Joseph Pasciak

Dept. of Mathematics,
Texas A&M University,
College Station, TX 77840

Abstract
In this talk I shall consider iterative algorithms of Uzawa type for
solving nonsymmetric linear block saddle-point problems of the form

| A B | |U| |F|
| | | | = | |
| B^t 0 | |P| |G|.

Specifically, I
will consider the case when the upper
left block ** A **is nonsymmetric linear operator with positive definite
symmetric part. Such systems
arise, for example, in certain discretizations of Navier-Stokes equations.
The main results of the talk are for an
inexact Uzawa algorithm. The classical Uzawa algorithm requires the
action of the inverse of the operator ** A **.
The inexact Uzawa
methods replace the action of the exact inverse of ** A **
with an ``incomplete''
or ``approximate'' evaluation of its action. In practice, this
is provided by a preconditioner for the symmetric part of ** A **
such as one
multigrid V-cycle. A convergence result for the inexact algorithm will
be reported which shows that the iterative algorithm is a
contraction in an appropriate norm. This norm convergence is achieved
without the assumption of a sufficiently accurate approximation to the
inverse of ** A **.
Applications of the inexact Uzawa method
to the numerical solution of steady state Navier-Stokes
equations will also be discussed.
WWW:http://www.math.tamu.edu/~pasciak.