Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
A Posteriori Error Estimators for the Stokes and Oseen Equations
SIAM Journal on Numerical Analysis
Preconditioning in H(div) and applications
Mathematics of Computation
Iterative methods for solving linear systems
Iterative methods for solving linear systems
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A Posteriori Error Estimation for Stabilized Mixed Approximations of the Stokes Equations
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Optimal Preconditioning for Raviart--Thomas Mixed Formulation of Second-Order Elliptic Problems
SIAM Journal on Matrix Analysis and Applications
Stopping criteria for iterations in finite element methods
Numerische Mathematik
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
SIAM Journal on Numerical Analysis
Preconditioning and convergence in the right norm
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
SIAM Journal on Scientific Computing
A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations
Applied Numerical Mathematics
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We discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural “energy” norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error. We describe a “proof of concept” MATLAB implementation of this algorithm, which we call EST_MINRES, and we illustrate its effectiveness when integrated into the Incompressible Flow Iterative Solution Software (IFISS) package (cf. ACM Transactions on Mathematical Software 33, Article 14, 2007).