A wavelet based space-time adaptive numerical method for partial differential equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 26 (1992) no. 7, p. 793-834 
@article{M2AN_1992__26_7_793_0,
     author = {Bacry, E. and Mallat, S. and Papanicolaou, G.},
     title = {A wavelet based space-time adaptive numerical method for partial differential equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {26},
     number = {7},
     year = {1992},
     pages = {793-834},
     zbl = {0768.65062},
     mrnumber = {1199314},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1992__26_7_793_0}
}

Bacry, E.; Mallat, S.; Papanicolaou, G. A wavelet based space-time adaptive numerical method for partial differential equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 26 (1992) no. 7, pp. 793-834. http://www.numdam.org/item/M2AN_1992__26_7_793_0/

[1] R. Bank, A multilevel iterative method for nonlinear elliptic equations, Elliptic Problem Solvers, M. Schultz, Ed., p. 1, Academic Press, New York, 1981. | Zbl 0467.65054

[2] G. Battle, A block spin construction of ondelettes, Comm. Math. Phys., 110, p. 601, 1987. | MR 895218

[3] M. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, J. Comp. Phys., 82 pp. 64-84, 1989. | Zbl 0665.76070

[4] M. Berger and J. Oliger, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, J. Comp. Phys., 53, No. 3, pp. 484-512, 1984. | MR 739112 | Zbl 0536.65071

[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. | MR 1191143 | Zbl 0766.65007

[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] A. Brandt, Math. Comp., 31, p. 333, 1977, New York, 1981. | MR 431719 | Zbl 0373.65054

[8] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. in Pure Apll. Math., 41, pp. 909-996, November 1988. | MR 951745 | Zbl 0644.42026

[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. | MR 969030 | Zbl 0694.35206

[10] P. G. Lemarie, Ondelettes à localisation exponentielles, J. Math. Pures Appl., 1988. | MR 964171 | Zbl 0758.42020

[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.

[12] S. Mallat, Multiresolution approximation and wavelet orthonormal bases of L2, Trans. Amer. Math. Soc. 315, pp. 69-87, Sept. 1989. | MR 1008470 | Zbl 0686.42018

[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. | Zbl 0709.94650

[14] Y. Meyer, Ondelettes et opérateurs, Hermann, Paris 1990. | MR 1085487 | Zbl 0694.41037

[15] Y. Meyer, Ondelettes orthogonales sur un interval, preprint CEREMADE, Université Paris Dauphine, 1991. | MR 1133374

[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. | Zbl 0521.46011

[17] J.-C. Xu andW.-C. Shann, Galerkin-wavelets Methods for Two-point Boundary Value Problems, preprint, May 1991. | Zbl 0771.65050

[18] H. Yserentant, On the multi-level splittmg of finite element spaces, Numer. Math., 49, pp. 379-412, 1986. | Zbl 0608.65065