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Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems
Publikationstyp
Journal Article
Publikationsdatum
2015-03-01
Sprache
English
Institut
TORE-URI
Enthalten in
Volume
16
Issue
6
Start Page
259
End Page
269
Citation
Computing and Visualization in Science 6 (16): 259-269 (2015)
Publisher DOI
Scopus ID
Publisher
Springer
This paper deals with the analysis of preconditioning techniques for a recently introduced sparse grad-div stabilization of the Oseen problem. The finite element discretization error for the Oseen problem can be reduced through the addition of a grad-div stabilization term to the momentum equation of the Oseen problem. Such a stabilization has an interesting effect on the properties of the discrete linear system of equations, in particular on the convergence properties of iterative solvers. Comparing to unstabilized systems, it swaps the levels of difficulties for solving the two main subproblems, i.e., solving for the first diagonal block and solving a Schur complement problem, that occur in preconditioners based on block triangular factorizations. In this paper we are concerned with a sparse variant of grad-div stabilization which has been shown to have a stabilization effect similar to the full grad-div stabilization while leading to a sparser system matrix. Our focus lies on the subsequent iterative solution of the discrete system of equations.
Schlagworte
augmented lagrangian
grad-div stabilization
oseen problem
preconditioner
schur complement
sparse grad-div
DDC Class
510: Mathematik