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
A preconditioned iterative method for saddlepoint problems
SIAM Journal on Matrix Analysis and Applications
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Approximate Inverse Techniques for Block-Partitioned Matrices
SIAM Journal on Scientific Computing
Accurate Symmetric Indefinite Linear Equation Solvers
SIAM Journal on Matrix Analysis and Applications
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
On Block Preconditioners for Nonsymmetric Saddle Point Problems
SIAM Journal on Scientific Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Preconditioners for saddle point problems arising in computational fluid dynamics
Applied Numerical Mathematics
Fast uzawa algorithm for generalized saddle point problems
Applied Numerical Mathematics
Block triangular preconditioners for symmetric saddle-point problems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
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The generalized Stokes problem is solved for non-standard boundary conditions. This problem arises after time semi-discretization by ALE method of the Navier-Stokes system, which describes the flow of two immiscible fluids with similar densities but different viscosities in a horizontal pipe, when modeling heavy crude oil transportation. We discretized the generalized Stokes problem in space using the ''Mini'' finite element. The inf-sup condition is proved when the interface between the two fluids and its discretization match exactly. The linear system obtained after discretization is solved using different iterative Krylov methods with and without preconditioning. Numerical experiments with different meshes are presented as well as comparisons between the methods considered. The results suggest that FGMRES and a preconditioning technique based on symmetric/skew-symmetric decomposition is a promising candidate for solving large scale generalized Stokes problem.