Adaptive wavelet methods for saddle point problems

Stephan Dahlke; Reinhard Hochmuth; Karsten Urban

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 5, page 1003-1022
  • ISSN: 0764-583X

How to cite

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Dahlke, Stephan, Hochmuth, Reinhard, and Urban, Karsten. "Adaptive wavelet methods for saddle point problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.5 (2000): 1003-1022. <http://eudml.org/doc/194018>.

@article{Dahlke2000,
author = {Dahlke, Stephan, Hochmuth, Reinhard, Urban, Karsten},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {adaptive schemes; saddle point problems; wavelets; multiscale methods; Uzawa's algorithm; a posteriori error estimates; numerical examples},
language = {eng},
number = {5},
pages = {1003-1022},
publisher = {Dunod},
title = {Adaptive wavelet methods for saddle point problems},
url = {http://eudml.org/doc/194018},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Dahlke, Stephan
AU - Hochmuth, Reinhard
AU - Urban, Karsten
TI - Adaptive wavelet methods for saddle point problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 5
SP - 1003
EP - 1022
LA - eng
KW - adaptive schemes; saddle point problems; wavelets; multiscale methods; Uzawa's algorithm; a posteriori error estimates; numerical examples
UR - http://eudml.org/doc/194018
ER -

References

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  1. [1] H.W. Alt, Lineare Funktionalanalysis (in german). Springer-Verlag, Berlin (1985). Zbl0577.46001
  2. [2] K. Arrow, L. Hurwicz and H. Uzawa, Studies in Nonlinear Programming Stanford University Press, Stanford, CA (1958). Zbl0091.16002MR108399
  3. [3] S. Bertoluzza, A posteriori error estimates for the wavelet Galerkin method. Appl. Math. Lett. 8 (1995) 1-6. Zbl0835.65121MR1356289
  4. [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). Zbl0859.76049MR1408777
  5. [5] D. Braess, Finite Elements Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, Cambridge (1997). Zbl0894.65054MR1463151
  6. [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. Zbl0873.65031MR1451114
  7. [7] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). Zbl0788.73002MR1115205
  8. [8] A. Cohen, Wavelet methods in Numerical Analysis, in: Handbook of Numerical Analysis, North Holland, Amsterdam (to appear). Zbl0976.65124MR1804747
  9. [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. [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. Zbl0872.65098MR1438079
  11. [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). Zbl0965.65074
  12. [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). Zbl0998.76067MR1786767
  13. [13] W. Dahmen, Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-361. Zbl0919.46006MR1395769
  14. [14] W. Dahmen, Wavelet and multiscale methods for operator equations. Acta Numerica 6 (1997) 55-228. Zbl0884.65106MR1489256
  15. [15] W. Dahmen, Wavelet methods for PDEs - Some recent developments, RWTH Aachen, IGPM Preprint 183 (1999). Zbl0974.65101MR1820873
  16. [16] W. Dahmen, A. Kunoth and K. Urban, A Wavelet-Galerkin method for the Stokes problem. Computing 56 (1996) 259-302. Zbl0849.65077MR1393010
  17. [17] H.C. Elman and G.H. Golub, Inexact and preconditioned Uzawa algorithme for saddle point problems. SIAM J. Numer. Anal.31 (1994) 1645-1661. Zbl0815.65041MR1302679
  18. [18] M. Fortin, Old and new Finite Elements for incompressible flows. Int. J. Numer. Meth. Fluids 1 (1981) 347-364. Zbl0467.76030MR633812
  19. [19] R. Hochmuth, Stable multiscale discretizations for saddle point problems and preconditioning. Numer. Funct. Anal. and Optimiz. 19 (1998) 789-806. Zbl0913.65113MR1642569
  20. [20] P.G. Lemarié-Rieusset, Analyses multi-résolutions non orthogonales, Commutation entre Projecteurs et Dérivation et Ondelettes Vecteurs à divergence nulle. Rev. Mat. Iberoam. 8 (1992) 221-236. Zbl0874.42022MR1191345
  21. [21] R. Masson, Wavelet discretizations of the Stokes problem in velocity-pressure variables, Preprint, Univ. P. et M. Curie, Paris (1998). 
  22. [22] K. Urban, On divergence-free wavelets. Adv. Comput. Math. 4 (1995) 51-82. Zbl0822.42020MR1338895
  23. [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) Zbl0963.65155MR1710628

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