Convergence analysis of a multigrid method for convection-diffusion equations

Numerische Mathematik

Volumn 91, Issue 2, 2002, Pages 323-349

  Reusken, Arnold ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036556997     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100312     Document Type: Article

References (30)

1. Bank, R.E., Benbourenane, M.: A Fourier analysis of the two-level hierarchical basis multigrid method for convection-diffusion equations. In: Proceedings of the Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, 1-8, SIAM, Philadelphia (1991)
2. Bank, R.E., Benbourenane, M.: The hierarchical basis multigrid method for convection-diffusion equations. Numer. Math. 61, 7-37 (1992)
3. Bey, J., Wittum, G.: Downwind numbering: robust multigrid for convection-diffusion problems. Appl. Numer. Math. 23, 177-192 (1997)
4. Börm, S., Hiptmair, R.: Analysis of tensor product multigrid. Preprint, Mathematisches Seminar, University of Kiel (1999)
5. Bramble, J.H.: Multigrid methods. Longman, Harlow (1993)
6. Bramble, J.H., Pasciak, J.E., Xu, J.: The analysis of multigrid algorithms for nonsymmetric and indefinite problems. Math. Comp. 51, 389-414 (1988)
7. Dendy, J.E. Jr.(1983): Black box multigrid for nonsymmetric problems. Appl. Math. Comput. 13, 261-283
8. Ecker, A., Zulehner, W.: On the smoothing property of multigrid methods in the nonsymmetric case. Numer. Linear Algebra Appl. 3, 161-172 (1996)
9. Hackbusch, W.: Multi-Grid Methods and Applications. Berlin: Springer 1985
10. Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. New York: Springer 1994
11. Hackbusch, W.: Multigrid convergence for a singular perturbation problem. Linear Algebra Appl. 58, 125-145 (1984)
12. Hackbusch, W.: A note on Reusken's Lemma. Computing 55, 181-189 (1995)
13. Hackbusch, W., T. Probst: Downwind Gauss-Seidel smoothing for convection dominated problems. Numer. Linear Algebra Appl. 4, 85-102 (1997)
14. Johannsen, K.: Robust smoothers for convection-diffusion problems. Preprint IWR, University of Heidelberg (1999)
15. Mandel, J.: Multigrid convergence for nonsymmetric, indefinite variational problems and one smoothing step. Appl. Math. Comput. 19, 201-216 (1986)
16. Mulder, W.: A new multigrid approach to convection problems. J. Comput. Phys. 83, 303-323 (1989)
17. Naik, N.H., van Rosedale, J.: The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids. SIAM Numer. Anal. 30, 215-229 (1993)
18. Persson, I., Samuelsson, K., Szepessy, A.: On the convergence of multigrid methods for flow problems. ETNA 8,46-87 (1999)
19. Pflaum, C.: Robust convergence of multilevel algorithms for convection-diffusion equations. SIAM J. Numer. Anal. 37, 443-469 (2000)
20. Reusken, A.: The smoothing property for regular splittings. In: Incomplete Decompositions (ILU)-Algorithms, Theory, and Applications. W. Hackbusch, G. Wittum (eds.), Vieweg, Braunschweig, 130-138 (1992)
21. Reusken, A.: Multigrid with matrix-dependent transfer operators for convection-diffusion problems. In: Multigrid Methods 4, Proceedings of the fourth multigrid conference. P.W. Hemker, P. Wesseling (eds.), International series of Numerical Mathematics 116, 269-280 (1994)
22. Reusken, A.: On maximum norm convergence of multigrid methods for two-point boundary value problems. SIAM J. Numer. Anal. 29, 1569-1578 (1992)
23. Reusken, A.: Multigrid with matrix-dependent transfer operators for a singular perturbation problem. Computing 50, 199-211 (1994)
24. Reusken, A.: Fourier analysis of a robust multigrid method for convection-diffusion equations. Numer. Math. 71, 365-397 (1995)
25. Roos, H.-G., M. Stynes, L. Tobiska: Numerical Methods for Singularly Perturbed Differential Equations. Berlin: Springer 1996
26. Wang, J.: Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems. SIAM J. Numer. Anal. 30, 275-285 (1993)
27. Wesseling, P.: An Introduction to Multigrid Methods. Chichester: Wiley 1992
28. Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581-613 (1992)
29. Yserentant, H.: Old and new convergence proofs for multigrid methods. Acta Numerica 1993, 285-326 (1993)
30. Zeeuw, P.M. de: Matrix-dependent prolongations and restrictions in a blackbox multigrid solver. J. Comput. Appl. Math. 33, 1-27 (1990)