Uzawa type algorithms for nonsymmetric saddle point problems

Mathematics of Computation

Volumn 69, Issue 230, 2000, Pages 667-689

  Bramble, James H ^a   Pasciak, Joseph E ^a   Vassilev, Apostol T ^a  

^a NONE

Author keywords

Indefinite systems; Iterative methods; Navier Stokes equations; Nonsymmetric saddle point systems; Oseen equations; Preconditioners; Saddle point problems; Uzawa algorithm

Indexed keywords

EID: 0040778237     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01152-7     Document Type: Article

References (32)

1. K. Arrow, L. Hurwicz, and H. Uzawa. Studies in Linear and Nonlinear Programming. Stanford University Press, Stanford, CA, 1958. MR 21:7115
2. K. Arrow, L. Hurwicz, and H. Uzawa. Studies in Linear and Nonlinear Programming. Stanford University Press, Stanford, CA, 1958. MR 21:7115
3. J.H. Bramble and J.E. Pasciak. A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Comp., 50:1-18, 1988; 51:387 388, 1988. MR 89m:65097
4. J.H. Bramble and J.E. Pasciak. A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Comp., 50:1-18, 1988; 51:387 388, 1988. MR 89m:65097
5. J.H. Bramble and J.E. Pasciak. A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems. Math. Comp., 50:1-18, 1988; 51:387 388, 1988. MR 89m:65097
6. J.H. Bramble and J.E. Pasciak. Iterative techniques for time dependent Stokes problems. Computers Math. Applic., 33:13-30, 1997. MR 98e:65091
7. J.H. Bramble and J.E. Pasciak. Iterative techniques for time dependent Stokes problems. Computers Math. Applic., 33:13-30, 1997. MR 98e:65091
8. J.H. Bramble, J.E. Pasciak, and A.T. Vassilev. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal., 34:1072-1092, 1997. MR 98c:65182
9. J.H. Bramble, J.E. Pasciak, and A.T. Vassilev. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal., 34:1072-1092, 1997. MR 98c:65182
10. F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991. MR 92d:65187
11. F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991. MR 92d:65187
12. P.G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, New York, 1978. MR 58:25001
13. P.G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, New York, 1978. MR 58:25001
14. H. Elman. Preconditioning for the steady-state Navier-Stokes equations with low viscosity. Technical Report CS-TR-3712, Department of Computer Science, University of Maryland, College Park, MD 20742, 1996.
15. H. Elman and D. Silvester. Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM J. Sci. Comput., 17:33-46, 1996. MR 97e:65119
16. H. Elman and D. Silvester. Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM J. Sci. Comput., 17:33-46, 1996. MR 97e:65119
17. V. Girault and P.A. Raviart. Finite Element, Approximation of the Navier-Stokes Equations. Lecture Notes in Math. # 749, Springer-Verlag, New York, 1981. MR 83b:65122
18. V. Girault and P.A. Raviart. Finite Element, Approximation of the Navier-Stokes Equations. Lecture Notes in Math. # 749, Springer-Verlag, New York, 1981. MR 83b:65122
19. C. Johnson and J. Pitkäranta. Analysis of some mixed finite element methods related to reduced integration. Math. Comp., 38:375-400, 1982. MR 83d:65287
20. C. Johnson and J. Pitkäranta. Analysis of some mixed finite element methods related to reduced integration. Math. Comp., 38:375-400, 1982. MR 83d:65287
21. O.A. Karakashian. On a Galerkin-Lagrange multiplier method for the stationary Navier-Stokes equations. SIAM J. Numer. Anal., 19:909-923, 1982. MR 83j:65107
22. O.A. Karakashian. On a Galerkin-Lagrange multiplier method for the stationary Navier-Stokes equations. SIAM J. Numer. Anal., 19:909-923, 1982. MR 83j:65107
23. C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. National Bureau of Standards, 45:255-282, 1950. MR 13:163d
24. C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. National Bureau of Standards, 45:255-282, 1950. MR 13:163d
25. J.L. Lions and E. Magenes. Problèmes aux Limites non Homogènes et Applications, volume 1. Dunod, Paris, 1968. MR 40:512
26. J.L. Lions and E. Magenes. Problèmes aux Limites non Homogènes et Applications, volume 1. Dunod, Paris, 1968. MR 40:512
27. M.M. Liu, J. Wang, and N.-N. Yan. New error estimates for approximate solutions of convection-diffusion problems by mixed and discontinuous Galerkin methods. SIAM J. Numer. Anal. Submitted.
28. M.F. Murphy and A. J. Wathen. On preconditioning for the Oseen equations. Technical Report AM 95-07, Department of Mathematics, University of Bristol, 1995.
29. Y. Saad and M.H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856-869, 1986. MR 87g:65064
30. Y. Saad and M.H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856-869, 1986. MR 87g:65064
31. R. Temam. Navier-Stokes Equations. North-Holland Publishing Co., New York, 1977. MR 58:29439
32. R. Temam. Navier-Stokes Equations. North-Holland Publishing Co., New York, 1977. MR 58:29439