GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Fast iterative solution of stabilised Stokes systems, part I: using simple diagonal preconditioners
SIAM Journal on Numerical Analysis
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
On the Nonlinear Inexact Uzawa Algorithm for Saddle-Point Problems
SIAM Journal on Numerical Analysis
An Efficient Linear Solver for Nonlinear Parameter Identification Problems
SIAM Journal on Scientific Computing
An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Fast uzawa algorithm for generalized saddle point problems
Applied Numerical Mathematics
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Nonlinear Inexact Uzawa Algorithms for Linear and Nonlinear Saddle-point Problems
SIAM Journal on Optimization
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
An Efficient Solver for the Incompressible Navier-Stokes Equations in Rotation Form
SIAM Journal on Scientific Computing
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
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This paper proposes a modified nonlinear inexact Uzawa (MNIU) algorithm for solving the stabilized saddle point problem, by introducing a variable overrelaxation parameter to speed up convergence. MNIU is an inner-outer iteration method with variable inner accuracy. We give a detailed error analysis for the convergence of MNIU, based upon a newly defined error norm which helps to handle variable inner accuracy for the Uzawa method. We also simply formulate the optimal overrelaxation parameter. Sufficient conditions are given for the convergence of MNIU. We show that MNIU converges in a relatively large range for the variable inner accuracy setting. For constant inner accuracy $\delta$, MNIU is convergent when $\delta