Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
A sufficient condition for the convergence of the inexact Uzawa algorithm for saddle point problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Fast Iterative Solution of Saddle Point Problems in Optimal Control Based on Wavelets
Computational Optimization and Applications
Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition
Journal of Scientific Computing
Preconditioners for saddle point problems arising in computational fluid dynamics
Applied Numerical Mathematics
Fast uzawa algorithm for generalized saddle point problems
Applied Numerical Mathematics
Analysis of iterative algorithms of Uzawa type for saddle point problems
Applied Numerical Mathematics
Overlapping Schwarz preconditioner for the mixed formulation of plane elasticity
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Limiting accuracy of segregated solution methods for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
On the convergence of iterative methods for stabilized saddle point problems
International Journal of Computer Mathematics
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Schur complements on Hilbert spaces and saddle point systems
Journal of Computational and Applied Mathematics
Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems
International Journal of Computer Mathematics
Large-Scale Scientific Computing
Journal of Computational and Applied Mathematics
Application of modified homotopy perturbation method for solving the augmented systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Overlapping Schwarz preconditioner for the mixed formulation of plane elasticity
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Multigrid-based optimal shape and topology design in magnetostatics
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Journal of Computational and Applied Mathematics
New choices of preconditioning matrices for generalized inexact parameterized iterative methods
Journal of Computational and Applied Mathematics
Residual reduction algorithms for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
SIAM Journal on Matrix Analysis and Applications
Modified homotopy perturbation method for solving the Stokes equations
Computers & Mathematics with Applications
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
Riemannian Newton Method for the Multivariate Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
SIAM Journal on Scientific Computing
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NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
The semi-convergence of generalized SSOR method for singular augmented systems
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Multilevel discretization of symmetric saddle point systems without the discrete LBB condition
Applied Numerical Mathematics
Mathematical and Computer Modelling: An International Journal
Preconditioned AHSS iteration method for singular saddle point problems
Numerical Algorithms
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Journal of Computational and Applied Mathematics
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems
Journal of Scientific Computing
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In this paper, we consider the so-called "inexact Uzawa" algorithm for iteratively solving linear block saddle point problems. Such saddle point problems arise, for example, in finite element and finite difference discretizations of Stokes equations, the equations of elasticity, and mixed finite element discretization of second-order problems. We consider both the linear and nonlinear variants of the inexact Uzawa iteration. We show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled. Bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned Uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left-hand block. In the case of nonlinear iteration, the inexact Uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left-hand block is of sufficient accuracy. Bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear Uzawa algorithm. Applications to the Stokes equations and mixed finite element discretization of second-order elliptic problems are discussed and, finally, the results of numerical experiments involving the algorithms are presented.