A wavelet based space-time adaptive numerical method for partial differential equations

 Access to full text

 Full (PDF)

1. [1] R. BANK, A multilevel iterative method for nonlinear elliptic equations, Elliptic Problem Solvers, M. Schultz, Ed., p. 1, Academic Press, New York, 1981. Zbl0467.65054
2. [2] G. BATTLE, A block spin construction of ondelettes, Comm. Math. Phys., 110, p. 601, 1987. MR895218
3. [3] M. BERGER and P. COLELLA, Local adaptive mesh refinement for shock hydrodynamics, J. Comp. Phys., 82 pp. 64-84, 1989. Zbl0665.76070
4. [4] M. BERGER and J. OLIGER, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, J. Comp. Phys., 53, No. 3, pp. 484-512, 1984. Zbl0536.65071MR739112
5. [5] G. BEYLKIN, On the representation of operators in bases of compactly supported wavelets, Proceedings of the École sur des Problèmes non Linéaires Appliqués, INRIA, Paris, June 1991. Zbl0766.65007MR1191143
6. [6] G. BEYLKIN, R. COFIMAN and V. ROKHLIN, Fast wavelet transform and numerical algorithms, Yale University Tech. Report YALE/DCS/RR-696, August 1989. 
7. [7] A. BRANDT, Math. Comp., 31, p. 333, 1977, New York, 1981. Zbl0373.65054MR431719
8. [8] I. DAUBECHIES, Orthonormal bases of compactly supported wavelets, Comm. in Pure Apll. Math., 41, pp. 909-996, November 1988. Zbl0644.42026MR951745
9. [9] B. LE MESURIER, G. PAPANICOLAOU, G. SULEM and P. SULEM, Local structure of the self focusing singularity of the nonlinear Schroedinger equation, Physica D, 32, pp. 210-226, 1988. Zbl0694.35206MR969030
10. [10] P. G. LEMARIE, Ondelettes à localisation exponentielles, J. Math. Pures Appl., 1988. Zbl0758.42020MR964171
11. [11] J. LIANDRAT and Ph. TCHAMITCHIAN, Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation, NASA Report, ICASE Report No. 90-83, Dec. 1990. Zbl0917.65117
12. [12] S. MALLAT, Multiresolution approximation and wavelet orthonormal bases of L2, Trans. Amer. Math. Soc. 315, pp. 69-87, Sept. 1989. Zbl0686.42018MR1008470
13. [13] S. MALLAT, A theory for multiresolution signal decomposition : the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell., 11, No. 7, pp. 674-693, July 1989. Zbl0709.94650
14. [14] Y. MEYER, Ondelettes et opérateurs, Hermann, Paris 1990. Zbl0694.41037MR1085487
15. [15] Y. MEYER, Ondelettes orthogonales sur un interval, preprint CEREMADE, Université Paris Dauphine, 1991. MR1133374
16. [16] J. STROMBERG, A modified Franklin system and higher-order Systems of Rn as unconditional bases for Hardy spaces, Conference in Harmonie Analysis in Honor of A. Zygmund, 2, pp 475-493, eds. W. Beckner et al., Wadsworth Math. Series. Zbl0521.46011
17. [17] J.-C. XU and W.-C. SHANN, Galerkin-wavelets Methods for Two-point Boundary Value Problems, preprint, May 1991. Zbl0771.65050
18. [18] H. YSERENTANT, On the multi-level splittmg of finite element spaces, Numer. Math., 49, pp. 379-412, 1986. Zbl0608.65065

1. Philippe Charton, Valérie Perrier, Produits rapides matrice-vecteur en bases d'ondelettes : application à la résolution numérique d'équations aux dérivés partielles