@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] 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
, , , , , and ,[2] Fast wavelet transforms and numerical algorithms I. Comm. Pure Appl. Math. 44 (1991) 141-183. | MR | Zbl
, and ,[3] 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
and ,[4] An adaptive spline wavelet ADI(SW-ADI) method for two-dimensional reaction diffusion equations. J. Comput. Phys. 139 (1998) 92-126. | MR | Zbl
and ,[5] The wavelet element method, part I: construction and analysis. Appl. Comput. Harmon. Anal 6 (1999) 1-52. | MR | Zbl
, and ,[6] The Finite Element Method for Elliptic Problems. Stud. Math. Appl. 4, North-Holland, Amsterdam (1978). | MR | Zbl
,[7] 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
, and ,[8] Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl Math. 45 (1992) 485-560. | MR | Zbl
, and ,[9] Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23 (1997) 21-48. | MR | Zbl
, , and ,[10] 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
, and ,[11] Stability of multiscale transformations. J. Fourier Anal. Appl. 2 (1996) 341-362. | MR | Zbl
,[12] Wavelet and multiscale methods for operator equations. Acta Numer. 6 (1997) 55-228. | MR | Zbl
,[13] Multiscale Wavelet Methods for Partial Differential Equations. Wavelet Anal. Appl. 6, Academic Press, San Diego (1997). | MR
, and Eds.,[14] Wavelet approximation methods for pseudodifferential equations. II Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335. | MR | Zbl
, and ,[15] Composite wavelet bases for operator equations. Math. Comp. 68 (1999) 1533-1567. | MR | Zbl
and ,[16] Element-by-element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal 37 (1999) 319-352. | MR | Zbl
and ,[17] Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 906-966. | MR | Zbl
,[18] Ten Lectures on Wavelets. CBMS-NSF Ser. in Appl. Math. 61, SIAM Publications, Philadelphia (1992). | MR | Zbl
,[19] An adaptive wavelet-Galerkin algorithm for one- and two-dimensional flame computations. Eur. J. Mech. B Fluids 11 (1994) 439-471. | MR | Zbl
and ,[20] An adaptive wavelet-vaguelette algorithm for the solution of nonlinear PDEs. J. Comput. Phys. 130 (1997) 174-190. | MR | Zbl
and ,[21] Numerical Methods for Nonlinear Variational Problems. Springer Ser. Comput. Phys., Springer-Verlag, New York (1984). | MR | Zbl
,[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 | Zbl
,[23] A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | MR | Zbl
, and ,[24] 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
, and ,[25] 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.
, and ,[26]Elliptic Differential Equations: Theory and Numerical Treatment. Springer Ser. Comput. Math. 18, Springer-Verlag, Heidelberg (1992). | MR | Zbl
,[27] Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal 29 (1992) 965-986. | MR | Zbl
,[28] Bases d'ondelettes dans des ouverts de Rn. J. Math. Pures Appl. 68 (1992) 95-108. | MR | Zbl
and ,[29] Wavelets: Theory and Applications. Pure Appl. Math., Wiley, Chichester (1997). | MR | Zbl
, and ,[30] Ondelettes et Opérateurs I: Ondelettes. Actualités Mathématiques, Hermann, Paris (1990). English version: Wavelets and Operators, Cambridge University Press (1992). | MR | Zbl
,[31] Multilevel solvers for elliptic problems on domains, in Dahmen et al. [13] 3-58. | MR
,[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
,[33] A domain embedding method for Dirichlet problems in arbitrary space dimension. RAIRO Modél. Math. Anal. Numér. 32 (1998) 405-431. | Numdam | MR | Zbl
,[34] Singular Integrais and Differentiability Properties of Functions. Princeton Math. Ser. 22, Princeton University Press, Princeton (1970). | MR | Zbl
,[35] Partial Differential Equations. Cambridge University Press, Cambridge, UK (1987). | MR | Zbl
,