Block preconditioning for saddle point systems with indefinite (1, 1) block
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Preconditioning and convergence in the right norm
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Short Note: New connections between finite element formulations of the Navier-Stokes equations
Journal of Computational Physics
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
Applied Numerical Mathematics
Journal of Computational Physics
A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations
Journal of Computational Physics
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Modified block preconditioners for the discretized time-harmonic Maxwell equations in mixed form
Journal of Computational and Applied Mathematics
A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Journal of Computational Physics
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We describe an effective solver for the discrete Oseen problem based on an augmented Lagrangian formulation of the corresponding saddle point system. The proposed method is a block triangular preconditioner used with a Krylov subspace iteration like BiCGStab. The crucial ingredient is a novel multigrid approach for the (1,1) block, which extends a technique introduced by Schoberl for elasticity problems to nonsymmetric problems. Our analysis indicates that this approach results in fast convergence, independent of the mesh size and largely insensitive to the viscosity. We present experimental evidence for both isoP2-P0 and isoP2-P1 finite elements in support of our conclusions. We also show results of a comparison with two state-of-the-art preconditioners, showing the competitiveness of our approach.