# Inexact Uzawa Algorithms for Nonsymmetric Saddle Point Problems

• James H. Brambley, Joseph E. Pasciaky
• Published 2007

#### Abstract

In this paper, we consider iterative algorithms of Uzawa type for solving linear nonsymmetric block saddle point problems. Speciically, we consider systems where the upper left block is invertable nonsymmetric linear operator with positive deenite symmetric part. Such saddle point problems arise, for example, in certain nite element and nite diierence discretizations of Navier{Stokes equations , Oseen equations, and mixed nite element discretization of second order convection-diiusion problems. We consider two algorithms which utilize an \in-complete" or \approximate" evaluation of the inverse of the operator in the upper left block. Convergence results for the inexact algorithms are established in appropriate norms. The convergence of one of the algorithms is shown without the assumption of a suuciently accurate approximation to the inverse operator. The other algorithm is shown to converge provided that the approximation to the inverse of the upper left hand block is of suucient accuracy. Applications to the solution of steady-state nonlinear Navier{Stokes equations are discussed and nally, the results of numerical experiments involving the algorithms are presented.

### Cite this paper

@inproceedings{Brambley2007InexactUA, title={Inexact Uzawa Algorithms for Nonsymmetric Saddle Point Problems}, author={James H. Brambley and Joseph E. Pasciaky}, year={2007} }