Fast Uzawa algorithms for solving non‐symmetric stabilized saddle point problems

Abstract

AbstractBramble et al. (Math. Comput. (2000); 69 (230) : 667–689) discussed the Uzawa type algorithms for iteratively solving nonsymmetric stable saddle point problems. In this paper, we consider the Uzawa type algorithms for iteratively solving generalized saddle point problems. Our main concern is how to accelerate the convergence of the inexact Uzawa type algorithms. The contributions of the paper are that a new non‐linear Uzawa type algorithm is presented and its convergence is analysed. Applications to Navier–Stokes equations by mixed finite element discretization with an unstable pair of approximation spaces, i.e. Q1‐P0 pair of approximation spaces, are discussed and the results of the numerical experiments of applying our new algorithm are presented. Copyright © 2003 John Wiley & Sons, Ltd.