Free Access
Volume 34, Number 6, November/December 2000
Page(s) 1189 - 1202
Published online 15 April 2002
  1. A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen and K. Urban, Adaptive wavelet schemes for elliptic problems: implementation and numerical experiments. Tech. Report 173, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, 52056 Aachen, Germany (1999).
  2. G. Beylkin, R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I. Comm. Pure Appl. Math. 44 (1991) 141-183. [CrossRef] [MathSciNet]
  3. J.H. Bramble and S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112-124. [CrossRef] [MathSciNet]
  4. W. Cai and W. Zhang, An adaptive spline wavelet ADI(SW-ADI) method for two-dimensional reaction diffusion equations. J. Comput. Phys. 139 (1998) 92-126. [CrossRef] [MathSciNet]
  5. C. Canuto, A. Tabacco and K. Urban, The wavelet element method, part I: construction and analysis. Appl. Comput. Harmon. Anal. 6 (1999) 1-52. [CrossRef] [MathSciNet]
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Stud. Math. Appl. 4, North-Holland, Amsterdam (1978).
  7. A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet methods for elliptic operator equations - convergence rates. Math. Comp. posted on May 23, 2000, PII S0025-5718(00)01252-7 (to appear in print).
  8. A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45 (1992) 485-560. [CrossRef] [MathSciNet]
  9. 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. [CrossRef] [MathSciNet]
  10. S. Dahlke, V. Latour and K. Gröchenig, Biorthogonal box spline wavelet bases, in Surface Fitting and Multiresolution Methods, A.L. Méhauté, C. Rabut and L.L. Schumaker Eds., Vanderbilt University Press (1997) 83-92.
  11. W. Dahmen, Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-362. [MathSciNet]
  12. W. Dahmen, Wavelet and multiscale methods for operator equations. Acta Numer. 6 (1997) 55-228. [CrossRef]
  13. W. Dahmen, A. Kurdila and P. Oswald Eds., Multiscale Wavelet Methods for Partial Differential Equations. Wavelet Anal. Appl. 6, Academic Press, San Diego (1997).
  14. W. Dahmen, S. Prössdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations. II. Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335. [CrossRef] [MathSciNet]
  15. W. Dahmen and R. Schneider, Composite wavelet bases for operator equations. Math. Comp. 68 (1999) 1533-1567. [CrossRef] [MathSciNet]
  16. W. Dahmen and R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal. 37 (1999) 319-352. [CrossRef] [MathSciNet]
  17. I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 906-966.
  18. I. Daubechies, Ten Lectures on Wavelets. CBMS-NSF Ser. in Appl. Math. 61, SIAM Publications, Philadelphia (1992).
  19. J. Fröhlich and K. Schneider, An adaptive wavelet-Galerkin algorithm for one- and two-dimensional flame computations. Eur. J. Mech. B Fluids 11 (1994) 439-471.
  20. J. Fröhlich and K. Schneider, An adaptive wavelet-vaguelette algorithm for the solution of nonlinear PDEs. J. Comput. Phys. 130 (1997) 174-190. [CrossRef] [MathSciNet]
  21. R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer Ser. Comput. Phys., Springer-Verlag, New York (1984).
  22. R. Glowinski, Finite element methods for the numerical simulation of incompressible viscous flow: Introduction to the control of the Navier-Stokes equations, in Vortex Dynamics and Vortex Methods, C.R. Anderson and C. Greengard Eds., Lectures in Appl. Math. 28, Providence, AMS (1991) 219-301.
  23. R. Glowinski, T.-W. Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. [CrossRef] [MathSciNet]
  24. R. Glowinski, T.-W. Pan and J. Périaux, A Lagrange multiplier/fictitious domain method for the Dirichlet problem - generalizations to some flow problems. Japan J. Indust. Appl. Math. 12 (1995) 87-108. [CrossRef] [MathSciNet]
  25. R. Glowinski, T.-W. Pan and J. Périaux, Fictitious domain methods for the simulation of Stokes flow past a moving disk, in Computational Fluid Dynamics '96, J.A. Desideri, C. Hirsh, P. LeTallec, M. Pandolfi and J. Périaux Eds., Chichester, Wiley (1996) 64-70.
  26. W. Hackbusch, Elliptic Differential Equations: Theory and Numerical Treatment. Springer Ser. Comput. Math. 18, Springer-Verlag, Heidelberg (1992).
  27. S. Jaffard, Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal. 29 (1992) 965-986. [CrossRef] [MathSciNet]
  28. S. Jaffard and Y. Meyer, Bases d'ondelettes dans des ouverts de Formula . J. Math. Pures Appl. 68 (1992) 95-108.
  29. A.K. Louis, P. Maass and A. Rieder, Wavelets: Theory and Applications. Pure Appl. Math., Wiley, Chichester (1997).
  30. Y. Meyer, Ondelettes et Opérateurs I: Ondelettes. Actualités Mathématiques, Hermann, Paris (1990). English version: Wavelets and Operators, Cambridge University Press (1992).
  31. P. Oswald, Multilevel solvers for elliptic problems on domains, in Dahmen et al. [] 3-58.
  32. A. Rieder, On embedding techniques for 2nd-order elliptic problems, in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Périaux and M.F. Wheeler Eds., Wiley, Chichester (1997) 179-188.
  33. A. Rieder, A domain embedding method for Dirichlet problems in arbitrary space dimension. RAIRO Modél. Math. Anal. Numér. 32 (1998) 405-431. [MathSciNet]
  34. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton Math. Ser. 22, Princeton University Press, Princeton (1970).
  35. J. Wloka, Partial Differential Equations. Cambridge University Press, Cambridge, UK (1987).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you