@article{M2AN_2000__34_6_1189_0,
author = {Rieder, Andreas},
title = {Embedding and a priori wavelet-adaptivity for Dirichlet problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {34},
year = {2000},
pages = {1189-1202},
mrnumber = {1812733},
zbl = {0985.65149},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2000__34_6_1189_0}
}
Rieder, Andreas. Embedding and a priori wavelet-adaptivity for Dirichlet problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 1189-1202. http://gdmltest.u-ga.fr/item/M2AN_2000__34_6_1189_0/
[1] , , , , , and , 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). | Zbl 1016.65090
[2] , and , Fast wavelet transforms and numerical algorithms I. Comm. Pure Appl. Math. 44 (1991) 141-183. | MR 1085827 | Zbl 0722.65022
[3] and , Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112-124. | MR 263214 | Zbl 0201.07803
[4] and , An adaptive spline wavelet ADI(SW-ADI) method for two-dimensional reaction diffusion equations. J. Comput. Phys. 139 (1998) 92-126. | MR 1611650 | Zbl 0905.65103
[5] , and , The wavelet element method, part I: construction and analysis. Appl. Comput. Harmon. Anal 6 (1999) 1-52. | MR 1664902 | Zbl 0949.42024
[6] , The Finite Element Method for Elliptic Problems. Stud. Math. Appl. 4, North-Holland, Amsterdam (1978). | MR 520174 | Zbl 0383.65058
[7] , and , 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). | MR 1803124 | Zbl 0980.65130
[8] , and , Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl Math. 45 (1992) 485-560. | MR 1162365 | Zbl 0776.42020
[9] , , and , Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23 (1997) 21-48. | MR 1438079 | Zbl 0872.65098
[10] , and , Biorthogonal box spline wavelet bases, in Surface Fitting and Multiresolution Meihods, A.L. Méhauté, C. Rabut and L.L. Schumaker Eds., Vanderbilt University Press (1997) 83-92. | MR 1660007 | Zbl 0946.65149
[11] , Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-362. | MR 1395769 | Zbl 0919.46006
[12] , Wavelet and multiscale methods for operator equations. Acta Numer. 6 (1997) 55-228. | MR 1489256 | Zbl 0884.65106
[13] , and Eds., Multiscale Wavelet Methods for Partial Differential Equations. Wavelet Anal. Appl. 6, Academic Press, San Diego (1997). | MR 1474995
[14] , and , Wavelet approximation methods for pseudodifferential equations. II Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335. | MR 1242378 | Zbl 0826.65093
[15] and , Composite wavelet bases for operator equations. Math. Comp. 68 (1999) 1533-1567. | MR 1648379 | Zbl 0932.65148
[16] and , Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal 37 (1999) 319-352. | MR 1742747 | Zbl 0942.65130
[17] , Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 906-966. | MR 951745 | Zbl 0644.42026
[18] , Ten Lectures on Wavelets. CBMS-NSF Ser. in Appl. Math. 61, SIAM Publications, Philadelphia (1992). | MR 1162107 | Zbl 0776.42018
[19] and , An adaptive wavelet-Galerkin algorithm for one- and two-dimensional flame computations. Eur. J. Mech. B Fluids 11 (1994) 439-471. | MR 1298062 | Zbl 0814.76068
[20] and , An adaptive wavelet-vaguelette algorithm for the solution of nonlinear PDEs. J. Comput. Phys. 130 (1997) 174-190. | MR 1433931 | Zbl 0868.65067
[21] , Numerical Methods for Nonlinear Variational Problems. Springer Ser. Comput. Phys., Springer-Verlag, New York (1984). | MR 737005 | Zbl 0536.65054
[22] , 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. | MR 1146474 | Zbl 0751.76046
[23] , and , A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | MR 1259864 | Zbl 0845.73078
[24] , and , A Lagrange multiplier/fictitious domain method for the Dirichlet problem - generalizations to some flow problems. Japan J. Indust. Appl. Math. 12 (1995) 87-108. | MR 1320642 | Zbl 0835.76047
[25] , and , 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], Elliptic Differential Equations: Theory and Numerical Treatment. Springer Ser. Comput. Math. 18, Springer-Verlag, Heidelberg (1992). | MR 1197118 | Zbl 0755.35021
[27] , Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal 29 (1992) 965-986. | MR 1173180 | Zbl 0761.65083
[28] and , Bases d'ondelettes dans des ouverts de Rn. J. Math. Pures Appl. 68 (1992) 95-108. | MR 985955 | Zbl 0704.46009
[29] , and , Wavelets: Theory and Applications. Pure Appl. Math., Wiley, Chichester (1997). | MR 1681147 | Zbl 0897.42019
[30] , Ondelettes et Opérateurs I: Ondelettes. Actualités Mathématiques, Hermann, Paris (1990). English version: Wavelets and Operators, Cambridge University Press (1992). | MR 1085487 | Zbl 0694.41037
[31] , Multilevel solvers for elliptic problems on domains, in Dahmen et al. [13] 3-58. | MR 1474996
[32] , On embedding techniques for 2nd-order elliptic problems, in Computational Science for the 2lst Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Périaux and M.F. Wheeler Eds., Wiley, Chichester (1997) 179-188. | Zbl 0911.65111
[33] , A domain embedding method for Dirichlet problems in arbitrary space dimension. RAIRO Modél. Math. Anal. Numér. 32 (1998) 405-431. | Numdam | MR 1636364 | Zbl 0913.65099
[34] , Singular Integrais and Differentiability Properties of Functions. Princeton Math. Ser. 22, Princeton University Press, Princeton (1970). | MR 290095 | Zbl 0207.13501
[35] , Partial Differential Equations. Cambridge University Press, Cambridge, UK (1987). | MR 895589 | Zbl 0623.35006