The Wavelet Element Method: Part I. Construction and Analysis

Applied and Computational Harmonic Analysis

Volumn 6, Issue 1, 1999, Pages 1-52

  Canuto, Claudio ^a,b   Tabacco, Anita ^a   Urban, Karsten ^c  

^a POLITECNICO DI TORINO   (Italy)

^b CNR   (Italy)

^c RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007372257     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1997.0242     Document Type: Article

References (35)

1. Adams R. A. Sobolev Spaces. 1978;Academic Press, San Diego.
2. Andersson L., Hall N., Jawerth B., Peters G. Wavelets on closed subsets of the real line. Topics in the Theory and Applications of Wavelets. 1994;Academic Press, Boston. p. 1-61.
3. Bertoluzza S. A posteriori error estimates for the wavelet Galerkin method. Appl. Math. Lett. 8:1995;1-6.
4. Beylkin G., Coifman R., Rokhlin V. Fast wavelet transforms and numerical algorithms. Comm. Pure Appl. Math. 44:1991;141-183.
5. Canuto C., Cravero I. A wavelet-based adaptive finite element method for the advection-diffusion equations. Math. Mod. Methods Appl. Sci. 7:1997;265-289.
6. Canuto C., Tabacco A. Multilevel decompositions of functional spaces. J. Fourier Anal. Appl. 3:1997;715-742.
7. C. Canuto, A. Tabacco, K. Urban, The wavelet element method. Part II. Realization and additional features in 2D and 3D, Dipartimento di Matematica, Politecnico di Torino, 1997.
8. Chiavassa G., Liandrat J. On the effective construction of compactly supported wavelets satisfying homogeneous boundary conditions on the interval. Appl. Comput. Harmon. Anal. 4:1997;62-73.
9. Ciarlet Ph. G. Basic error estimates for elliptic problems. Ciarlet Ph. G., Lions J. L. Handbook of Numerical Analysis, Vol. II. Finite Element Methods. 1991;17-351 North-Holland, Amsterdam.
10. A. Cohen, W. Dahmen, R. A. DeVore, Multiscale decompositions on bounded domains, Trans. Amer. Math. Soc.
11. Cohen A., Daubechies I., Feauveau J.-C. Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math. 45:1992;485-560.
12. Cohen A., Daubechies I., Vial P. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1:1993;54-81.
13. Dahlke S., Dahmen W., Hochmuth R., Schneider R. Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23:1997;21-48.
14. S. Dahlke, W. Dahmen, R. DeVore, Nonlinear approximation and adaptive techniques for solving elliptic operator equations, in, Multiscale Wavelet Methods for PDEs, W. DahmenA. KurdillaP. Oswald, Academic Press, San Diego, 237, 283.
15. Dahlke S., Weinreich I. Wavelet bases adapted to pseudo-differential operators. Appl. Comput. Harmon. Anal. 1:1994;267-283.
16. Dahmen W. Stability of multiscale transformations. J. Fourier Anal. Appl. 4:1996;341-362.
17. Dahmen W. Wavelet and multiscale methods for operator equations. Acta Numer. 1997;55-228.
18. Dahmen W., Kunoth A. Multilevel preconditioning. Numer. Math. 63:1992;315-344.
19. Dahmen W., Kunoth A., Urban K. A Wavelet-Galerkin method for the Stokes problem. Computing. 56:1996;259-302.
20. W. Dahmen, A. Kunoth, K. Urban, Biorthogonal spline-wavelets on the interval - Stability and moment conditions, Appl. Comput. Harmon. Anal.
21. Dahmen W., Prössdorf S., Schneider R. Multiscale methods for pseudo-differential equations on smooth manifolds. Chui C. K., Montefusco L., Puccio L. Proceedings of the International Conference on Wavelets: Theory, Algorithms, and Applications. 1994;385-424 Academic Press, San Diego.
22. W. Dahmen, R. Schneider, Composite wavelet bases for operator equations, 1996.
23. I. Daubechies, Ten lectures on wavelets, in, CBMS-NSF Regional Conference Series in Applied Mathematics, 61, Soc. for Industr. & Appl. Math. Philadelphia, 1992.
24. Jaffard S. Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal. 29:1992;965-986.
25. Jouini A., Lemarié-Rieusset P.-G. Analyses multirésolutions biorthogonales et applications. Ann. Inst. H. Poincaré Anal. Non Linéaire. 10:1993;453-476.
26. Lemarié-Rieusset P. G. Analyses multi-résolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle. Rev. Mat. Iberoamericana. 8:1992;221-236.
27. L. Levaggi, A. Tabacco, Wavelets on the interval and related topics, Dipartimento di Matematica, Politecnico di Torino, 1997.
28. J. Liandrat, Ph. Tchamitchian, Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation, 1990.
29. Maday Y., Patera A. T. Spectral element methods for the incompressible Navier-Stokes equations. Noor A. K., Oden J. T. State of the Art Surveys in Computational Mechanics. 1989;71-144 ASME, New York.
30. Maday Y., Perrier V., Ravel J. C. Adaptativité dynamique sur bases d'ondelettes pour l'approximation d'équations aux dérivées partielles. C. R. Acad. Sci. Paris Sér. I. 312:1991;405-410.
31. Meyer Y. Ondelettes. Vol. I. Ondelettes et Opèrateurs. 1990;Hermann, Paris.
32. Patera A. T. A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys. 54:1984;468-488.
33. Strang G., Nguyen T. Wavelets and Filter Banks. 1996;Wellesley Cambridge Press, Cambridge.
34. Urban K. On divergence-free wavelets. Adv. Comput. Math. 4:1995;51-82.
35. Wickerhauser M. V. Adapted Wavelet Analysis from Theory to Software. 1994;AK Peters, Wellesley.