Adaptive wavelet methods for saddle point problems

Mathematical Modelling and Numerical Analysis

Volumn 34, Issue 5, 2000, Pages 1003-1022

  Dahlke, Stephan ^a   Hochmuth, Reinhard ^b   Urban, Karsten ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

A posteriori error estimates; Adaptive schemes; Multiscale methods; Saddle point problems; Uzawa's algorithm; Wavelets

Indexed keywords

EID: 0034356805     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2000113     Document Type: Article

References (23)

1. H.W. Alt, Lineare Funktionalanalysis (in german). Springer Verlag, Berlin (1985).
2. K. Arrow, L. Hurwicz and H. Uzawa, Studies in Nonlinear Programming. Stanford University Press, Stanford, CA (1958).
3. S. Bertoluzza, A posteriori error estimates for the wavelet Galerkin method. Appl. Math. Lett. 8 (1995) 1-6.
4. S. Bertoluzza and R. Masson, Espaces vitesses pression d'ondelettes adaptives satisfaisant la condition Inf-Sup. C. R. Acad. Sci. Paris, Sér. Math. 323 (1996).
5. D. Braess, Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, Cambridge (1997).
6. 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 (1997) 1072-1092.
7. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991).
8. A. Cohen, Wavelet methods in Numerical Analysis, in: Handbook of Numerical Analysis, North Holland, Amsterdam (to appear).
9. A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet schemes for elliptic operator equations Convergence rates, RWTH Aachen, IGPM Preprint 165, 1998. Math. Comput. (to appear).
10. S. Dahlke, W. Dahmen, R. Hochmuth and R. Schneider, Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23 (1997) 21-48.
11. S. Dahlke, R. Hochmuth and K. Urban, Adaptive wavelet methods for saddle point problems, Preprint 1126, Istituto di Analisi Numerica del C. N. R. (1999).
12. S. Dahlke, R. Hochmuth and K. Urban, Convergent Adaptive Wavelet Methods for the Stokes Problem, in: Multigrid Methods VI, E. Dick, K. Riemslagh, J. Vierendeels Eds., Springer-Verlag (2000).
13. W. Dahmen, Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-361.
14. W. Dahmen, Wavelet and multiscale methods for operator equations. Acta Numerica 6 (1997) 55-228.
15. W. Dahmen, Wavelet methods for PDEs Some recent developments, RWTH Aachen, IGPM Preprint 183 (1999).
16. W. Dahmen, A. Kunoth and K. Urban, A Wavelet-Galerkin method for the Stokes problem. Computing 56 (1996) 259-302.
17. H.C. Elman and G.H. Golub, Inexact and preconditioned Uzawa algorithms for saddle point problems. SIAM J. Numer. Anal. 31 (1994) 1645-1661.
18. M. Fortin, Old and new Finite Elements for incompressible flows. Int. J. Numer. Meth. Fluids 1 (1981) 347-364.
19. R. Hochmuth, Stable multiscale discretizations for saddle point problems and preconditioning. Numer. Funct. Anal. and Optimiz. 19 (1998) 789-806.
20. P.G. Lemarié-Rieusset, Analyses multi-résolutions non orthogonales, Commutation entre Projecteurs et Derivation et On-delettes Vecteurs à divergence nulle. Rev. Mat. Iberoam. 8 (1992) 221-236.
21. R. Masson, Wavelet discretizations of the Stokes problem in velocity-pressure variables, Preprint, Univ. P. et M. Curie, Paris (1998).
22. K. Urban, On divergence-free wavelets. Adv. Comput. Math. 4 (1995) 51-82.
23. K. Urban, Wavelet bases in H(div) and H(curl), Preprint 1106, Istituto di Analisi Numerica del C. N. R., 1998. Math. Comput. (to appear).