Tchebychev iteration may be used for acceleration convergence of an iterative algorithm to solve a general linear system equation. Associating it with the Uzawa method, we suggest a new iterative solution method for the Stokes problems. The new algorithm retains the simplicity and robustness of the Uzawa method. So it requires almost no additional cost of computation, in terms of storage or CPU...

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixedpoint iteration, we explore the use of Anderson acceleration (also knownas Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleratio...

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method...

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to se...

As an extension of the inexact Uzawa algorithm addressed in 1], we propose an improved inexact Uzawa-type iterative method for solving saddle point problems. The convergence rate is given in terms of the rates of the two basic iterations as deened in 1], and it is shown that the new algorithm always converges as long as the two basic iterations converge. A running title: Uzawa algorithm for sad...

In this paper we present and analyze Uzawa type algorithms for solving discretized variational inequalities arising from two phase Stefan type problems. For a Uzawa type algorithm and its improved version we show convergence and derive bounds on convergence rates. For the improved Uzawa algorithm, the convergence rate is shown to be uniformly bounded away from 1 if τh−2 is kept bounded, with τ ...

In this note, we discuss the convergence behavior of a modified inexact Uzawa algorithm for solving generalized saddle point problems, which is an extension of the result obtained in a recent paper [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math., 46 (2003) 157-171]. Keywords—Saddle point problem; Inexact Uzawa algorithm; Convergence behavior.

Recently, various Uzawa methods were proposed based on different matrix splitting for solving nonsingular saddle point problems, and the necessary and sufficient condition of the convergence for those Uzawa methods were derived. Motivated by their results, in this paper we give the semi-convergence analysis of the inexact Uzawa method which is applied to solve singular saddle point problems und...

Different variants of the Uzawa algorithm are compared with one another. The comparison is performed for the case in which this algorithm is applied to large-scale systems of linear algebraic equations. These systems arise in the finite-element solution of the problems of elasticity theory for incompressible materials. A modification of the Uzawa algorithm is proposed. Computational experiments...

In this paper we discuss inexact Uzawa algorithms and inexact nonlinear Uzawa algorithms to solve discretized variational inequalities of the second kind. We prove convergence results for the algorithms. Numerical examples are included to show the effectiveness of the algorithms.