An adaptive wavelet-vaguelette algorithm for the solution of PDEs

Journal of Computational Physics

Volumn 130, Issue 2, 1997, Pages 174-190

  Fröhlich, Jochen ^a,c   Schneider, Kai ^b,c  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; WAVELET DECOMPOSITION;

ADAPTIVE WAVELETS; BASE FUNCTION; BIORTHOGONAL WAVELET; DISCRETIZATIONS; FAST ALGORITHMS; LACUNARY; ORTHONORMAL WAVELET TRANSFORMS; PRIORI INFORMATION; SCALING FUNCTIONS; WAVELET BASIS;

INVERSE PROBLEMS;

EID: 0031568188     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.5573     Document Type: Article

References (51)

1. Arandiga F., Candela V. F., Donat R. SIAM J. Sci. Comput. 6:1995;581.
2. Bacry E., Mallat S., Papanicolaou G. Math. Mod. Num. Anal. 26:1992;793.
3. Bertoluzza S., Naldi G. Comp. Appl. Math. 13:1994;13.
4. S. Bertoluzza, G. Naldi, 1994, Università di Pavia.
5. Bertoluzza S., Naldi G. Appl. Comp. Harm. Anal. 3:1996;1.
6. Beylkin G., Coifman R., Rokhlin V. Comm. Pure Appl. Math. 44:1991;141.
7. G. Beylkin, 1993, Progress in Wavelet Analysis and Applications, Proceedings of the International Conference Wavelets and Applications, Toulouse, 1992, 259, Editions Frontiers, Gif-sur-Yvette.
8. H. Bockhorn, J. Fröhlich, K. Schneider, 1996.
9. Brand R., Freeden W., Fröhlich J. Computing. 57:1996;187.
10. Buckmaster J. D., Ludford G. S. S. Theory of Laminar Flames. 1982;Cambridge Univer. Press, Cambridge.
11. Cai W., Wang J. SIAM J. Numer. Anal. 33:1996;937.
12. Charton Ph., Perrier V. RAIRO Modél. Math. Anal. Numeŕ 29:1995;701.
13. Chui C. K. An Introduction to Wavelets. 1992;Academic Press, Boston.
14. Chui C. K., Shi X. Lyche T., Schumaker L. L. Mathematical Methods in Computer-Aided Geometric Design. 1992;111 Academic Press, San Diego.
15. Dahlke S., Weinreich I. Constr. Approx. 9:1993;237.
16. Dahmen W., Kunoth A. Numer. Math. 63:1992;315.
17. Daubechies I. Ten Lectures on Wavelets. 1992;SIAM, Philadelphia.
18. Denet B., Haldenwang P. Combust. Sci. and Tech. 86:1992;199.
19. Deslauriers G., Dubuc S. Constr. Approx. 5:1989;49.
20. D. L. Donoho, 1992, Stanford University.
21. Engquist B., Osher S., Zhong S. SIAM J. Sci. Comput. 15:1994;755.
22. Fröhlich J., Schneider K. Europ. J. Mech., B/Fluids. 13:1994;439.
23. J. Fröhlich, K. Schneider, 1995, University Kaiserslautern.
24. Appl. Comp. Harm. Anal.
25. S. Gomes, C. Cuncha, 1995, Universidade de Campinas, Brazil.
26. Harten A. Comm. Pure Appl. Math. 48:1995;1305.
27. Harten A. SIAM J. Numer. Anal. 33:1996;1205.
28. Jaffard S. C.R. Acad. Sci. Paris I. 308:1989;79.
29. Jaffard S. SIAM J. Numer. Anal. 29:1992;965.
30. Jawerth B., Sweldens W. SIAM Rev. 36:1994;377.
31. Lazaar S., Liandrat J., Tchamitchian Ph. C.R. Acad.Sci. Paris I. 319:1994;1101.
32. Lemarié P. G. Rev. Math. Iberoamericana. 7:1991;157.
33. Lemarié-Rieusset P. G., Malgouyres G. Meyer Y. Wavelets and Applications. 1992;Masson, Paris.
34. J. Liandrat, Ph. Tchamitchian, 1990, ICASE.
35. Maday Y., Perrier V., Ravel J.Ch. C.R. Acad.Sci. Paris I. 312:1991;405.
36. Maday Y., Ravel J.Ch. C.R. Acad.Sci. Paris I. 315:1992;85.
37. Maz'ya V. Whiteman J. R. The Mathematics of Finite Elements and Applications. Highlights 1993. 1994;Wiley, New York.
38. Meyer Y. Ondelettes et Opérateurs I/II. 1990;Hermann, Paris.
39. Perrier V., Basdevant C. Rech. Aérosp. 3:1989;53.
40. Plantevin F. Advances in Comp. Math. 4:1995;293.
41. P. Ponenti, 1994, University Aix-Marseille I.
42. Qian Z., Weiss J. J. Comput. Phys. 106:1993;155.
43. Ronney P. Combust. Flame. 82:1990;1.
44. Schoenberg I. J. J. Approx. Theory. 2:1969;167.
45. Sivashinski G. I. Acta Astronaut. 4:1977;1177.
46. Stein E. M., Weiss G. Fourier Analysis on Euclidian Spaces. 1971;Princeton Univer. Press, Princeton.
47. W. Sweldens, 1994, IMI, Dept. of Math. Univ. of South Carolina.
48. Sweldens W., Piessens R. SIAM J. Numer. Anal. 31:1994;1240.
49. Tchamitchian Ph. Rev. Mat. Iberoamericana. 3:1987;163.
50. Vasilyev O. V., Paolucci S., Sen M. J. Comput. Phys. 120:1995;33.
51. Walter G. IEEE Trans. Inform. Theory. 38:1992;881.