메뉴 건너뛰기




Volumn 2, Issue 3, 2002, Pages 203-245

Adaptive Wavelet Methods II - Beyond the Elliptic Case

Author keywords

Adaptive methods; Best N term approximation; Convergence rates; Fast matrix vector multiplication; Indefinite problems; Operator equations; Quasi sparse matrices and vectors

Indexed keywords

ADAPTIVE METHODS; BEST N-TERM APPROXIMATION; CONVERGENCE RATES; INDEFINITE PROBLEMS; MATRIX VECTOR MULTIPLICATION; OPERATOR EQUATION;

EID: 0347937165     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s102080010027     Document Type: Article
Times cited : (191)

References (38)
  • 1
    • 84966251556 scopus 로고
    • Least-squares methods for elliptic systems
    • A. K. Aziz, R. B. Kellogg, and A. B. Stephens, Least-squares methods for elliptic systems, Math. Comp. 44 (1985), 53-70.
    • (1985) Math. Comp. , vol.44 , pp. 53-70
    • Aziz, A.K.1    Kellogg, R.B.2    Stephens, A.B.3
  • 2
    • 34250459417 scopus 로고
    • The finite element method with Lagrange multipliers
    • I. Babuška, The finite element method with Lagrange multipliers, Numer. Math. 20 (1973), 179-192.
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuška, I.1
  • 5
    • 0000102411 scopus 로고    scopus 로고
    • Stabilization by multiscale decomposition
    • S. Bertoluzza, Stabilization by multiscale decomposition, Appl. Math. Lett. 11 (1998), 129-134.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 129-134
    • Bertoluzza, S.1
  • 6
    • 0034207727 scopus 로고    scopus 로고
    • On the adaptive computation of integrals of wavelets
    • S. Bertoluzza, C. Canuto, and K. Urban, On the adaptive computation of integrals of wavelets, Appl. Numer. Math. 34 (2000), 13-38.
    • (2000) Appl. Numer. Math. , vol.34 , pp. 13-38
    • Bertoluzza, S.1    Canuto, C.2    Urban, K.3
  • 8
    • 0031518552 scopus 로고    scopus 로고
    • A least-squares approach based on a discrete minus one inner product for first-order systems
    • J. H. Bramble, R. D. Lazarov, and J. E. Pasciak, A least-squares approach based on a discrete minus one inner product for first-order systems, Math. Comp. 66 (1997), 935-955.
    • (1997) Math. Comp. , vol.66 , pp. 935-955
    • Bramble, J.H.1    Lazarov, R.D.2    Pasciak, J.E.3
  • 10
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations for elliptic problems
    • J. H. Bramble and J. E. Pasciak, A preconditioning technique for indefinite systems resulting from mixed approximations for elliptic problems. Math. Comp. 50 (1988), 1-17.
    • (1988) Math. Comp. , vol.50 , pp. 1-17
    • Bramble, J.H.1    Pasciak, J.E.2
  • 11
    • 84968466812 scopus 로고
    • Least squares methods for 2mth-order elliptic boundary-value problems
    • J. H. Bramble and A. H. Schatz, Least squares methods for 2mth-order elliptic boundary-value problems, Math. Comp. 25 (1971), 1-32.
    • (1971) Math. Comp. , vol.25 , pp. 1-32
    • Bramble, J.H.1    Schatz, A.H.2
  • 13
    • 0028747782 scopus 로고
    • First-order system least squares for second-order partial differential equations, Part I
    • Z. Cai, R. Lazarov, T. A. Manteuffel, and S. F. McCormick, First-order system least squares for second-order partial differential equations, Part I, SIAM J. Numer. Anal. 31 (1994), 1785-1799.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1785-1799
    • Cai, Z.1    Lazarov, R.2    Manteuffel, T.A.3    McCormick, S.F.4
  • 14
    • 0000260120 scopus 로고    scopus 로고
    • First-order system least squares for the Stokes equations, with application to linear elasticity
    • Z. Cai, T. A. Manteuffel, and S. F. McCormick, First-order system least squares for the Stokes equations, with application to linear elasticity, SIAM J. Numer. Anal. 34 (1997), 1727-1741.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1727-1741
    • Cai, Z.1    Manteuffel, T.A.2    McCormick, S.F.3
  • 15
    • 0007372257 scopus 로고    scopus 로고
    • The wavelet element method. Part I: Construction and analysis
    • A. Canuto, A. Tabacco, and K. Urban, The wavelet element method. Part I: Construction and analysis, Appl. Comput. Harmonic Anal. 6 (1999), 1-52.
    • (1999) Appl. Comput. Harmonic Anal. , vol.6 , pp. 1-52
    • Canuto, A.1    Tabacco, A.2    Urban, K.3
  • 16
    • 0003369980 scopus 로고    scopus 로고
    • Wavelets in numerical analysis
    • (P. G. Ciarlet and J. L. Lions eds.), Elsevier, Amsterdam
    • A. Cohen, Wavelets in numerical analysis, in Handbook of Numerical Analysis, Vol. VII (P. G. Ciarlet and J. L. Lions eds.), Elsevier, Amsterdam, 1999.
    • (1999) Handbook of Numerical Analysis , vol.7
    • Cohen, A.1
  • 17
    • 0035606214 scopus 로고    scopus 로고
    • Adaptive wavelet methods for elliptic operator equations - Convergence rates
    • A. Cohen, W. Dahmen, and R. A. DeVore, Adaptive wavelet methods for elliptic operator equations - Convergence rates, Math. Comp. 70 (2001), 27-75.
    • (2001) Math. Comp. , vol.70 , pp. 27-75
    • Cohen, A.1    Dahmen, W.2    DeVore, R.A.3
  • 18
    • 0034413389 scopus 로고    scopus 로고
    • Wavelet adaptive methods for second-order elliptic problems, boundary conditions and domain decomposition
    • A. Cohen and R. Masson, Wavelet adaptive methods for second-order elliptic problems, boundary conditions and domain decomposition, Numer. Math. 86 (2000), 193-238,
    • (2000) Numer. Math. , vol.86 , pp. 193-238
    • Cohen, A.1    Masson, R.2
  • 19
    • 0025505601 scopus 로고
    • Coupling of finite and boundary element methods for an elastoplastic interface problem
    • M. Costabel and E. P. Stephan, Coupling of finite and boundary element methods for an elastoplastic interface problem, SIAM J. Numer. Anal. 27 (1990), 1212-1226.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 1212-1226
    • Costabel, M.1    Stephan, E.P.2
  • 20
    • 0031069391 scopus 로고    scopus 로고
    • Stable multiscale bases and local error estimation for elliptic problems
    • S. Dahlke, W. Dahmen, R. Hochmuth, and R. Schneider, Stable multiscale bases and local error estimation for elliptic problems, Appl. Numer. Math. 8 (1997), 21-47.
    • (1997) Appl. Numer. Math. , vol.8 , pp. 21-47
    • Dahlke, S.1    Dahmen, W.2    Hochmuth, R.3    Schneider, R.4
  • 21
    • 0141645585 scopus 로고    scopus 로고
    • Adaptive wavelet methods for saddle point problems -Convergence rates
    • IGPM Report # 204, RWTH Aachen, July 2001, to appear
    • S. Dahlke, W. Dahmen, and K. Urban, Adaptive wavelet methods for saddle point problems -Convergence rates, IGPM Report # 204, RWTH Aachen, July 2001, to appear in SIAM J. Numer. Anal.
    • SIAM J. Numer. Anal.
    • Dahlke, S.1    Dahmen, W.2    Urban, K.3
  • 22
    • 0034356805 scopus 로고    scopus 로고
    • Adaptive wavelet methods for saddle point problems
    • M2AN
    • S. Dahlke, R. Hochmuth, and K. Urban, Adaptive wavelet methods for saddle point problems, Math. Model. Numer. Anal. (M2AN), 34(5), (2000), 1003-1022.
    • (2000) Math. Model. Numer. Anal. , vol.34 , Issue.5 , pp. 1003-1022
    • Dahlke, S.1    Hochmuth, R.2    Urban, K.3
  • 23
    • 85011480386 scopus 로고    scopus 로고
    • Wavelet and multiscale methods for operator equations
    • W. Dahmen, Wavelet and multiscale methods for operator equations, Acta Numerica 6 (1997), 55-228.
    • (1997) Acta Numerica , vol.6 , pp. 55-228
    • Dahmen, W.1
  • 24
    • 0035280516 scopus 로고    scopus 로고
    • Wavelet methods for PDEs - Some recent developments
    • W. Dahmen, Wavelet methods for PDEs - Some recent developments, J. Comput. Appl. Math. 128 (2001), 133-185.
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 133-185
    • Dahmen, W.1
  • 25
    • 0035585768 scopus 로고    scopus 로고
    • Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition
    • W. Dahmen and A. Kunoth, Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition, Numer. Math. 88 (2001), 9-42; 215 (1994), 583-620.
    • (2001) Numer. Math. , vol.88 , pp. 9-42
    • Dahmen, W.1    Kunoth, A.2
  • 26
    • 0035585768 scopus 로고    scopus 로고
    • W. Dahmen and A. Kunoth, Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition, Numer. Math. 88 (2001), 9-42; 215 (1994), 583-620.
    • (1994) Numer. Math. , vol.215 , pp. 583-620
  • 27
    • 0009552360 scopus 로고    scopus 로고
    • Wavelet least squares methods for boundary value problems
    • IGPM Report # 175, RWTH Aachen, Sept. to appear
    • W. Dahmen, A. Kunoth, and R. Schneider, Wavelet least squares methods for boundary value problems, IGPM Report # 175, RWTH Aachen, Sept. 1999, to appear in SIAM J. Numer. Anal.
    • (1999) SIAM J. Numer. Anal.
    • Dahmen, W.1    Kunoth, A.2    Schneider, R.3
  • 28
    • 0033426280 scopus 로고    scopus 로고
    • Composite wavelet bases for operator equations
    • W. Dahmen and R. Schneider, Composite wavelet bases for operator equations, Math. Comp. 68 (1999), 1533-1567.
    • (1999) Math. Comp. , vol.68 , pp. 1533-1567
    • Dahmen, W.1    Schneider, R.2
  • 29
    • 0033233501 scopus 로고    scopus 로고
    • Wavelets on manifolds I: Construction and domain decomposition
    • W. Dahmen and R. Schneider, Wavelets on manifolds I: Construction and domain decomposition, SIAM J. Math. Anal. 31 (1999), 184-230.
    • (1999) SIAM J. Math. Anal. , vol.31 , pp. 184-230
    • Dahmen, W.1    Schneider, R.2
  • 30
    • 0000930347 scopus 로고    scopus 로고
    • Element-by-element construction of wavelets - Stability and moment conditions
    • W. Dahmen and R. Stevenson, Element-by-element construction of wavelets - Stability and moment conditions, SIAM J. Numer. Anal. 37 (1999), 319-325.
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 319-325
    • Dahmen, W.1    Stevenson, R.2
  • 31
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • R. DeVore, Nonlinear approximation, Acta Numerica 7 (1998), 51-150.
    • (1998) Acta Numerica , vol.7 , pp. 51-150
    • DeVore, R.1
  • 32
    • 0003269221 scopus 로고
    • Boundary-Field Equation Methods for a Class of Nonlinear Problems
    • Wiley, New York
    • G. N. Gatica and G. C. Hsiao, Boundary-Field Equation Methods for a Class of Nonlinear Problems, Pitman Research Notes in Mathematics Series, Vol. 331, Wiley, New York, 1995.
    • (1995) Pitman Research Notes in Mathematics Series , vol.331
    • Gatica, G.N.1    Hsiao, G.C.2
  • 34
    • 0001217594 scopus 로고
    • Error analysis of a fictitious domain method applied to a Dirichlet problem
    • R. Glowinski and V. Girault, Error analysis of a fictitious domain method applied to a Dirichlet problem, Japan J. Indust. Appl. Math. 12 (1995), 487-514.
    • (1995) Japan J. Indust. Appl. Math. , vol.12 , pp. 487-514
    • Glowinski, R.1    Girault, V.2
  • 35
    • 0026843540 scopus 로고
    • Treating inhomogeneous boundary conditions in finite element methods and the calculation of boundary stresses
    • M. D. Gunzburger and S. L. Hou, Treating inhomogeneous boundary conditions in finite element methods and the calculation of boundary stresses, SIAM J. Numer. Anal. 29 (1992), 390-424.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 390-424
    • Gunzburger, M.D.1    Hou, S.L.2
  • 36
    • 0001594654 scopus 로고
    • Multilevel preconditioning - Appending boundary conditions by Lagrange multipliers
    • A. Kunoth, Multilevel preconditioning - Appending boundary conditions by Lagrange multipliers. Adv. in Comput. Math. 4 (1995), 145-170.
    • (1995) Adv. in Comput. Math. , vol.4 , pp. 145-170
    • Kunoth, A.1
  • 38
    • 0004021335 scopus 로고
    • Grundlehren, Springer-Verlag, Berlin
    • K. Yosida, Functional Analysis, Grundlehren, Springer-Verlag, Berlin, 1966.
    • (1966) Functional Analysis
    • Yosida, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.