Embedding and a priori wavelet-adaptivity for Dirichlet problems
ESAIM: Modélisation mathématique et analyse numérique, Volume 34 (2000) no. 6, pp. 1189-1202.
@article{M2AN_2000__34_6_1189_0,
     author = {Rieder, Andreas},
     title = {Embedding and a priori wavelet-adaptivity for {Dirichlet} problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1189--1202},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {6},
     year = {2000},
     mrnumber = {1812733},
     zbl = {0985.65149},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_2000__34_6_1189_0/}
}
TY  - JOUR
AU  - Rieder, Andreas
TI  - Embedding and a priori wavelet-adaptivity for Dirichlet problems
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2000
SP  - 1189
EP  - 1202
VL  - 34
IS  - 6
PB  - Dunod
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_2000__34_6_1189_0/
LA  - en
ID  - M2AN_2000__34_6_1189_0
ER  - 
%0 Journal Article
%A Rieder, Andreas
%T Embedding and a priori wavelet-adaptivity for Dirichlet problems
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2000
%P 1189-1202
%V 34
%N 6
%I Dunod
%C Paris
%U http://archive.numdam.org/item/M2AN_2000__34_6_1189_0/
%G en
%F M2AN_2000__34_6_1189_0
Rieder, Andreas. Embedding and a priori wavelet-adaptivity for Dirichlet problems. ESAIM: Modélisation mathématique et analyse numérique, Volume 34 (2000) no. 6, pp. 1189-1202. http://archive.numdam.org/item/M2AN_2000__34_6_1189_0/

[1] A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen and K. Urban, 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

[2] G. Beylkin, R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I. Comm. Pure Appl. Math. 44 (1991) 141-183. | MR | Zbl

[3] J.H. Bramble and S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112-124. | MR | Zbl

[4] W. Cai and W. Zhang, An adaptive spline wavelet ADI(SW-ADI) method for two-dimensional reaction diffusion equations. J. Comput. Phys. 139 (1998) 92-126. | MR | Zbl

[5] C. Canuto, A. Tabacco and K. Urban, The wavelet element method, part I: construction and analysis. Appl. Comput. Harmon. Anal 6 (1999) 1-52. | MR | Zbl

[6] P.G. Ciarlet, The Finite Element Method for Elliptic Problems. Stud. Math. Appl. 4, North-Holland, Amsterdam (1978). | MR | Zbl

[7] A. Cohen, W. Dahmen and R. Devore, 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 | Zbl

[8] A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl Math. 45 (1992) 485-560. | MR | Zbl

[9] S. Dahlke, W. Dahmen, R. Hochmuth and R. Schneider, Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23 (1997) 21-48. | MR | Zbl

[10] S. Dahlke, V. Latour and K. Gröchenig, 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 | Zbl

[11] W. Dahmen, Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-362. | MR | Zbl

[12] W. Dahmen, Wavelet and multiscale methods for operator equations. Acta Numer. 6 (1997) 55-228. | MR | Zbl

[13] W. Dahmen, A. Kurdila and P. Oswald Eds., Multiscale Wavelet Methods for Partial Differential Equations. Wavelet Anal. Appl. 6, Academic Press, San Diego (1997). | MR

[14] W. Dahmen, S. Prössdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations. II Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335. | MR | Zbl

[15] W. Dahmen and R. Schneider, Composite wavelet bases for operator equations. Math. Comp. 68 (1999) 1533-1567. | MR | Zbl

[16] W. Dahmen and R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal 37 (1999) 319-352. | MR | Zbl

[17] I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 906-966. | MR | Zbl

[18] I. Daubechies, Ten Lectures on Wavelets. CBMS-NSF Ser. in Appl. Math. 61, SIAM Publications, Philadelphia (1992). | MR | Zbl

[19] J. Fröhlich and K. Schneider, An adaptive wavelet-Galerkin algorithm for one- and two-dimensional flame computations. Eur. J. Mech. B Fluids 11 (1994) 439-471. | MR | Zbl

[20] J. Fröhlich and K. Schneider, An adaptive wavelet-vaguelette algorithm for the solution of nonlinear PDEs. J. Comput. Phys. 130 (1997) 174-190. | MR | Zbl

[21] R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer Ser. Comput. Phys., Springer-Verlag, New York (1984). | MR | Zbl

[22] R. Glowinski, 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 | Zbl

[23] R. Glowinski, T.-W. Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | MR | Zbl

[24] R. Glowinski, T.-W. Pan and J. Périaux, 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 | Zbl

[25] R. Glowinski, T.-W. Pan and J. Périaux, 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]W. Hackbusch, Elliptic Differential Equations: Theory and Numerical Treatment. Springer Ser. Comput. Math. 18, Springer-Verlag, Heidelberg (1992). | MR | Zbl

[27] S. Jaffard, Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal 29 (1992) 965-986. | MR | Zbl

[28] S. Jaffard and Y. Meyer, Bases d'ondelettes dans des ouverts de Rn. J. Math. Pures Appl. 68 (1992) 95-108. | MR | Zbl

[29] A.K. Louis, P. Maass and A. Rieder, Wavelets: Theory and Applications. Pure Appl. Math., Wiley, Chichester (1997). | MR | Zbl

[30] Y. Meyer, Ondelettes et Opérateurs I: Ondelettes. Actualités Mathématiques, Hermann, Paris (1990). English version: Wavelets and Operators, Cambridge University Press (1992). | MR | Zbl

[31] P. Oswald, Multilevel solvers for elliptic problems on domains, in Dahmen et al. [13] 3-58. | MR

[32] A. Rieder, 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

[33] A. Rieder, , A domain embedding method for Dirichlet problems in arbitrary space dimension. RAIRO Modél. Math. Anal. Numér. 32 (1998) 405-431. | Numdam | MR | Zbl

[34] E.M. Stein, Singular Integrais and Differentiability Properties of Functions. Princeton Math. Ser. 22, Princeton University Press, Princeton (1970). | MR | Zbl

[35] J. Wloka, Partial Differential Equations. Cambridge University Press, Cambridge, UK (1987). | MR | Zbl