메뉴 건너뛰기




Volumn 70, Issue 233, 2001, Pages 27-75

Adaptive wavelet methods for elliptic operator equations: Convergence rates

Author keywords

Adaptive space refinement; Best N term approximation; Convergence rates; Elliptic operator equations; Fast matrix vector multiplication; Quasi sparse matrices and vectors; Thresholding

Indexed keywords


EID: 0035606214     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-00-01252-7     Document Type: Article
Times cited : (360)

References (42)
  • 2
    • 0023306715 scopus 로고
    • A feedback finite element method with a-posteriori error estimation: Part I. The finite element method and some basic properties of the a-posteriori error estimator
    • MR 88d:73036
    • I. Babuška and A. Miller, A feedback finite element method with a-posteriori error estimation: Part I. The finite element method and some basic properties of the a-posteriori error estimator, Comput. Methods Appl. Mech. Engrg. 61 (1987), 1-40. MR 88d:73036
    • (1987) Comput. Methods Appl. Mech. Engrg. , vol.61 , pp. 1-40
    • Babuška, I.1    Miller, A.2
  • 3
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • MR 58:3400
    • I. Babuška and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978), 736-754. MR 58:3400
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 4
    • 0002641609 scopus 로고
    • Refinement algorithms and data structures for regular local mesh refinement
    • R. Stepleman et al. (eds.), Amsterdam: IMACS, North-Holland, MR 851:00014
    • R.E. Bank, A.H. Sherman and A. Weiser, Refinement algorithms and data structures for regular local mesh refinement, in: R. Stepleman et al. (eds.), Scientific Computing, Amsterdam: IMACS, North-Holland, 1983, 3-17. MR 851:00014
    • (1983) Scientific Computing , pp. 3-17
    • Bank, R.E.1    Sherman, A.H.2    Weiser, A.3
  • 5
    • 84966215690 scopus 로고
    • Some a posteriori error estimates for elliptic partial differential equations
    • MR 86g:65207
    • R.E. Bank and A. Weiser, Some a posteriori error estimates for elliptic partial differential equations, Math. Comp., 44 (1985), 283-301. MR 86g:65207
    • (1985) Math. Comp. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 7
    • 33845201716 scopus 로고
    • A-posteriori error estimates for wavelet Galerkin methods
    • MR 96e:65053
    • S. Bertoluzza, A-posteriori error estimates for wavelet Galerkin methods, Appl Math. Lett., 8 (1995), 1-6. MR 96e:65053
    • (1995) Appl Math. Lett. , vol.8 , pp. 1-6
    • Bertoluzza, S.1
  • 8
    • 37949010323 scopus 로고    scopus 로고
    • An adaptive collocation method based on interpolating wavelets
    • W. Dahmen, A. J. Kurdila, P. Oswald (eds.), Academic Press, San Diego, MR 98d:65149
    • S. Bertoluzza, An adaptive collocation method based on interpolating wavelets, in: Multiscale Wavelet Methods for PDEs, W. Dahmen, A. J. Kurdila, P. Oswald (eds.), Academic Press, San Diego, 1997, 109-135. MR 98d:65149
    • (1997) Multiscale Wavelet Methods for PDEs , pp. 109-135
    • Bertoluzza, S.1
  • 9
    • 0034375557 scopus 로고    scopus 로고
    • Wavelet stabilization of the Lagrange multiplier method
    • S. Bertoluzza, Wavelet stabilization of the Lagrange multiplier method, to appear in Numcr. Math.
    • Numcr. Math.
    • Bertoluzza, S.1
  • 10
    • 0005591256 scopus 로고    scopus 로고
    • On the adaptive computation of integrals of wavelets
    • Preprint No. 1129, Istituto di Analisi Numerica del C.N.R. Pavia
    • S. Bertoluzza, C. Canuto, K. Urban, On the adaptive computation of integrals of wavelets, Preprint No. 1129, Istituto di Analisi Numerica del C.N.R. Pavia, 1999, to appear in Appl. Numer. Anal.
    • (1999) Appl. Numer. Anal.
    • Bertoluzza, S.1    Canuto, C.2    Urban, K.3
  • 11
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms I
    • MR 92c:65061
    • G. Beylkin, R. R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure and Appl. Math., 44 (1991), 141-183. MR 92c:65061
    • (1991) Comm. Pure and Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.R.2    Rokhlin, V.3
  • 12
    • 0041981841 scopus 로고    scopus 로고
    • An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations
    • W. Dahmen, A. J. Kurdila, P. Oswald (eds.), Academic Press, San Diego, MR, 98i:65124
    • G. Beylkin and J. M. Keiser, An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations, in: Multiscale Wavelet Methods for PDEs, W. Dahmen, A. J. Kurdila, P. Oswald (eds.), Academic Press, San Diego, 1997, 137-197. MR, 98i:65124
    • (1997) Multiscale Wavelet Methods for PDEs , pp. 137-197
    • Beylkin, G.1    Keiser, J.M.2
  • 13
    • 0001701058 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic problems in two and three space dimensions
    • MR 98a:65161
    • F. Bornemann, B. Erdmann, and R. Kornhuber, A posteriori error estimates for elliptic problems in two and three space dimensions, SIAM J. Numer. Anal., 33 (1996), 1188-1204. MR 98a:65161
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1188-1204
    • Bornemann, F.1    Erdmann, B.2    Kornhuber, R.3
  • 17
    • 33846966749 scopus 로고    scopus 로고
    • Wavelet methods in numerical analysis
    • A. Cohen, Wavelet methods in Numerical Analysis, to appear in the Handbook of Numerical Analysis, vol. VII, 1998.
    • (1998) The Handbook of Numerical Analysis , vol.7
    • Cohen, A.1
  • 18
    • 0040478221 scopus 로고    scopus 로고
    • Wavelet adaptive methods for elliptic equations - Preconditioning and aclaptivity
    • Preprint, LAN, Université Pierre et Marie Curie, Paris
    • A. Cohen arid R. Masson, Wavelet adaptive methods for elliptic equations - Preconditioning and aclaptivity, Preprint, LAN, Université Pierre et Marie Curie. Paris, 1997, to appear in SIAM J. Sci. Comp.
    • (1997) SIAM J. Sci. Comp.
    • Cohen, A.1    Masson, R.2
  • 19
    • 77957168971 scopus 로고    scopus 로고
    • Nonlinear approximation and adaptive techniques for solving elliptic equations
    • W. Dahmen, A. Kurdila, and P. Oswald (eds), Academic Press, San Diego, MR 99a:65001
    • S. Dahlke, W. Dahmen, and R. DeVore, Nonlinear approximation and adaptive techniques for solving elliptic equations, in: Multiscale Techniques for PDEs, W. Dahmen, A. Kurdila, and P. Oswald (eds), Academic Press, 1997, San Diego, 237-284. MR 99a:65001
    • (1997) Multiscale Techniques for PDEs , pp. 237-284
    • Dahlke, S.1    Dahmen, W.2    DeVore, R.3
  • 20
    • 0031069391 scopus 로고    scopus 로고
    • Stable multiscale bases and local error estimation for elliptic problems
    • MR 98a:65075
    • S. Dahlke, W. Dahmen, R. Hochmuth, and R. Schneider, Stable multiscale bases and local error estimation for elliptic problems, Applied Numerical Mathematics, 23 (1997), 21-47. MR 98a:65075
    • (1997) Applied Numerical Mathematics , vol.23 , pp. 21-47
    • Dahlke, S.1    Dahmen, W.2    Hochmuth, R.3    Schneider, R.4
  • 21
    • 0002494590 scopus 로고    scopus 로고
    • Besov regularity for elliptic boundary value problems
    • MR 97k:35047
    • S. Dahlke and R. DeVore, Besov regularity for elliptic boundary value problems, Communications in PDEs, 22(1997), 1-16. MR 97k:35047
    • (1997) Communications in PDEs , vol.22 , pp. 1-16
    • Dahlke, S.1    DeVore, R.2
  • 23
    • 85011480386 scopus 로고    scopus 로고
    • Wavelet and multiscale methods for operator equations
    • Cambridge University Press, MR 98m:65102
    • W. Dahmen, Wavelet and multiscale methods for operator equations, Acta Numerica 6, Cambridge University Press, 1997, 55-228. MR 98m:65102
    • (1997) Acta Numerica , vol.6 , pp. 55-228
    • Dahmen, W.1
  • 25
    • 0001783331 scopus 로고    scopus 로고
    • Multigrid and multiscale decompositions
    • M. Griebel, O.P. Iliev. S.D. Margenov, and P.S. Vassilevski, eds., Notes on Numerical Fluid Mechanics, Vieweg, Braunschweig/Wiesbaden, MR 2000b:65228
    • W. Dahmen, S. Müller, and T. Schlinkmann, Multigrid and multiscale decompositions, in: Large-Scale Scientific Computations of Engineering and Environmental Problems, M. Griebel, O.P. Iliev. S.D. Margenov, and P.S. Vassilevski, eds., Notes on Numerical Fluid Mechanics, Vol. 62, Vieweg, Braunschweig/Wiesbaden, 1998, 18-41. MR 2000b:65228
    • (1998) Large-scale Scientific Computations of Engineering and Environmental Problems , vol.62 , pp. 18-41
    • Dahmen, W.1    Müller, S.2    Schlinkmann, T.3
  • 31
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • Campbridge University Press, CMP 99:16
    • R. DeVore, Nonlinear approximation, Acta Numerica 7, Campbridge University Press, 1998, 51-150. CMP 99:16
    • (1998) Acta Numerica , vol.7 , pp. 51-150
    • DeVore, R.1
  • 32
    • 0001220724 scopus 로고
    • Compression of wavelet decompositions
    • MR 94a:42045
    • R. DeVore, B. Jawerth and V. Popov, Compression of wavelet decompositions, Amer. J. Math., 114 (1992), 737-785. MR 94a:42045
    • (1992) Amer. J. Math. , vol.114 , pp. 737-785
    • DeVore, R.1    Jawerth, B.2    Popov, V.3
  • 33
    • 0001604851 scopus 로고    scopus 로고
    • Interpolation spaces and nonlinear approximation
    • Function Spaces and Approximation, M. Cwikel et al, eds., Springer, MR 89d:41035
    • R. DeVore, V. Popov, Interpolation spaces and nonlinear approximation, in: Function Spaces and Approximation, M. Cwikel et al, eds., Lecture Notes in Mathematics, vol.1302, 1998, Springer, 191-205. MR 89d:41035
    • (1998) Lecture Notes in Mathematics , vol.1302 , pp. 191-205
    • DeVore, R.1    Popov, V.2
  • 35
    • 1542639888 scopus 로고    scopus 로고
    • A convergent adaptive algorithm for Poisson's equation
    • MR 97e:65139
    • W. Dörfler, A convergent adaptive algorithm for Poisson's equation, SIAM J. Numer. Anal., 33 (1996), 1106-1124. MR 97e:65139
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1106-1124
    • Dörfler, W.1
  • 36
    • 0009522795 scopus 로고
    • Introduction to adaptive methods for differential equations
    • Cambridge University Press, MR 96k:65057
    • K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Introduction to adaptive methods for differential equations, Acta Numerica 4, Cambridge University Press, (1995), 105-158. MR 96k:65057
    • (1995) Acta Numerica , vol.4 , pp. 105-158
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 37
    • 0003292476 scopus 로고
    • Littlewood-Paley theory and the study of function spaces
    • (AMS, Providence, RI), MR 92m:42021
    • M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley theory and the study of function spaces, CBMS Conference Lecture Notes 79, (AMS, Providence, RI), 1991. MR 92m:42021
    • (1991) CBMS Conference Lecture Notes , vol.79
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 38
    • 0004180195 scopus 로고
    • Hermann, Paris, MR 93i:42002; MR 931:42003
    • Y. Meyer, Ondelettes et Operateurs, Vol 1 and 2, Hermann, Paris, 1990. MR 93i:42002; MR 931:42003
    • (1990) Ondelettes et Operateurs , vol.1-2
    • Meyer, Y.1
  • 39
    • 0030242131 scopus 로고    scopus 로고
    • On the power of adaptation
    • E. Novak, On the power of adaptation, J. Complexity, 12(1996), 199-237.
    • (1996) J. Complexity , vol.12 , pp. 199-237
    • Novak, E.1
  • 40
    • 77957232248 scopus 로고    scopus 로고
    • Fully discrete multiscale Galerkin BEM
    • W. Dahmen, A. Kurdila, and P. Oswald (eds.), Academic Press, San Diego, MR 99a:65158
    • T. von Petersdorff, and C. Schwab, Fully discrete multiscale Galerkin BEM, in: Multiscale Wavelet Methods for PDEs, W. Dahmen, A. Kurdila, and P. Oswald (eds.), Academic Press, San Diego, 1997, 287-346. MR 99a:65158
    • (1997) Multiscale Wavelet Methods for PDEs , pp. 287-346
    • Von Petersdorff, T.1    Schwab, C.2
  • 42
    • 0005620566 scopus 로고    scopus 로고
    • Wavelets, functions, and operators
    • G. Erlebacher, M.Y. Hussaini, and L. Jameson (eds.), ICASE/LaRC Series in Computational Science and Engineering, Oxford University Press
    • P. Tchamitchian, Wavelets, Functions, and Operators, in: Wavelets: Theory and Applications, G. Erlebacher, M.Y. Hussaini, and L. Jameson (eds.), ICASE/LaRC Series in Computational Science and Engineering, Oxford University Press, 1996, 83-181.
    • (1996) Wavelets: Theory and Applications , pp. 83-181
    • Tchamitchian, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.