Block triangular preconditioners for nonsymmetric saddle point problems: Field-of-values analysis

Numerische Mathematik

Volumn 81, Issue 4, 1999, Pages 577-594

  Klawonn, Axel ^a   Starke, Gerhard ^b  

^a UNIVERSITY OF MÜNSTER   (Germany)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033483960     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050405     Document Type: Article

References (19)

1. Brezzi, F., Fortin, M. (1991): Mixed and Hybrid Finite Element Methods. Springer, New York
2. Eiermann, M. (1993): Fields of values and iterative methods. Linear Algebra Appl. 180, 167-198
3. Eisenstat, S.C., Elman, H.C., Schultz, M.H. (1983): Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Numer. Anal. 20, 345-357
4. Elman, H.C. (1982): Iterative Methods for Large, Sparse, Nonsymmetric Systems of Linear Equations. PhD thesis, Yale University
5. Elman, H.C. (1996): Preconditioning for the steady-state Navier-Stokes equations with low viscosity. Report CS-TR-3712, UMIACS-TR-96-82, University of Maryland
6. Elman, H.C., Silvester, D. (1996): Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM J. Sci. Comput. 17, 33-46
7. Golub, G.H., Wathen, A.J. (1998): An iteration for indefinite systems and its application to the Navier-Stokes equations. SIAM J. Sci. Comput. 19(2), 530-539
8. Gunzburger, M. (1989): Finite Element Methods for Viscous Incompressible Flows. Academic Press, San Diego
9. Horn, R.A., Johnson, C.R. (1991): Topics in Matrix Analysis. Cambridge University Press, Cambridge
10. Klawonn, A. (1998): Block triangular preconditioners for saddle point problems with a penalty term. SIAM J. Sci. Comput. 19(1), 172-184
11. Klawonn, A. (1998): An optimal preconditioner for a class of saddle point problems with a penalty term. SIAM J. Sci. Comput. 19(2), 540-552
12. Pavarino, L.F. (1998): Preconditioned mixed spectral element methods for elasticity and Stokes problems. SIAM J. Sci. Comput. 19(6), 1941-1957
13. Rusten, T., Winther, R. (1992): A preconditioned iterative method for saddle point problems. SIAM J. Matrix Anal. Appl. 13, 887-904
14. Saad, Y., Schultz, M.H. (1986): GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856-869
15. Silvester, D., Wathen, A.J. (1996): Fast and robust solvers for time-discretised incompressible Navier-Stokes equations. In: Griffiths, D.F., Watson, G.A. (eds.) Numerical Analysis 1995, pages 154-168. Addison Wesley Longman
16. Starke, G. (1996): Multilevel minimal residual methods for nonsymmetric elliptic problems. Numer. Linear Algebra Appl. 3, 351-367
17. Starke, G. (1997): Field-of-values-analysis of preconditioned iterative methods for non-symmetric elliptic problems. Numer. Math. 78, 103-117
18. Verfürth, R. (1984): A combined conjugate gradient multi-grid algorithm for the numerical solution of the Stokes problem. IMA J. Numer. Anal. 4, 441-455
19. Verfürth, R. (1984): A multilevel algorithm for mixed problems. SIAM J. Numer. Anal. 21, 264-271