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Volumn 38, Issue 3, 2001, Pages 1034-1055

Stable discretizations of convection-diffusion problems via computable negative-order inner products

Author keywords

Convection diffusion problems; Multiscale decompositions; Singularly perturbed problems; Stabilized Galerkin methods; Wavelets

Indexed keywords


EID: 0034436852     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999362298     Document Type: Article
Times cited : (25)

References (26)
  • 1
    • 0008803371 scopus 로고
    • Defect correction methods for convection-dominated convection-diffusion equations
    • O. AXELSSON AND W. LAYTON, Defect correction methods for convection-dominated convection-diffusion equations, RAIRO Modél. Math. Numer. Anal., 24 (1990), pp. 423-455.
    • (1990) RAIRO Modél. Math. Numer. Anal. , vol.24 , pp. 423-455
    • Axelsson, O.1    Layton, W.2
  • 2
    • 0142065075 scopus 로고
    • Un teorema di interpolazione; applicazioni ai problemi ai limiti per le equazioni a derivate parziali
    • C. BAIOCCHI, Un teorema di interpolazione; applicazioni ai problemi ai limiti per le equazioni a derivate parziali, Ann. Mat. Pura Appl., 73 (1966), pp. 235-252.
    • (1966) Ann. Mat. Pura Appl. , vol.73 , pp. 235-252
    • Baiocchi, C.1
  • 3
    • 0015727120 scopus 로고
    • Perturbations singulieres et prolongements maximaux d'operateurs positives
    • C. BARDOS, D. BREZIS, AND H. BREZIS, Perturbations singulieres et prolongements maximaux d'operateurs positives, Arch. Rational Mech. Anal., 53 (1973), pp. 69-100.
    • (1973) Arch. Rational Mech. Anal. , vol.53 , pp. 69-100
    • Bardos, C.1    Brezis, D.2    Brezis, H.3
  • 4
    • 0000102411 scopus 로고    scopus 로고
    • Stabilization by multiscale decomposition
    • S. BERTOLUZZA, Stabilization by multiscale decomposition, Appl. Math. Lett., 11 (1998), pp. 129-134.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 129-134
    • Bertoluzza, S.1
  • 5
    • 0000493139 scopus 로고    scopus 로고
    • Negative norm stabilization of convection-diffusion problems
    • S. BERTOLUZZA, C. CANUTO, AND A. TABACCO, Negative norm stabilization of convection-diffusion problems, Appl. Math. Lett., 13 (2000), pp. 121-127.
    • (2000) Appl. Math. Lett. , vol.13 , pp. 121-127
    • Bertoluzza, S.1    Canuto, C.2    Tabacco, A.3
  • 6
    • 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. LARAZOV, AND J. E. PASCIAK, A least-squares approach based on a discrete minus one inner product for first order systems, Math. Comp., 66 (1997), pp. 935-955.
    • (1997) Math. Comp. , vol.66 , pp. 935-955
    • Bramble, J.H.1    Larazov, R.D.2    Pasciak, J.E.3
  • 7
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 55 (1990), pp. 1-22.
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 8
    • 0026853555 scopus 로고
    • A relationship between stabilized finite element methods and the Galerkin method with bubble functions
    • F. BREZZI, M.-O BRISTEAU, L. FRANCA, M. MALLET, AND G. ROGÈR, A relationship between stabilized finite element methods and the Galerkin method with bubble functions, Comput. Methods Appl. Mech. Engrg., 96 (1992), pp. 117-129.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.96 , pp. 117-129
    • Brezzi, F.1    Bristeau, M.-O.2    Franca, L.3    Mallet, M.4    Rogèr, G.5
  • 10
    • 0034400351 scopus 로고    scopus 로고
    • Residual-free bubbles for advection-diffusion problems: The general error analysis
    • F. BREZZI, D. MARINI, AND E. SULI, Residual-free bubbles for advection-diffusion problems: The general error analysis, Numer. Math, 85 (2000), pp. 31-47.
    • (2000) Numer. Math , vol.85 , pp. 31-47
    • Brezzi, F.1    Marini, D.2    Suli, E.3
  • 11
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov Galerkin formulations for convective-dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A. N. BROOKS AND T. J. R. HUGHES, Streamline upwind/Petrov Galerkin formulations for convective-dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 32 (1982), pp. 199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 12
    • 0007372257 scopus 로고    scopus 로고
    • The Wavelet Element Method, Part I: Construction and analysis
    • C. CANUTO, A. TABACCO, AND K. URBAN, The Wavelet Element Method, Part I: Construction and analysis, Appl. Comput. Harm. Anal., 6 (1999), pp. 1-52.
    • (1999) Appl. Comput. Harm. Anal. , vol.6 , pp. 1-52
    • Canuto, C.1    Tabacco, A.2    Urban, K.3
  • 13
    • 84990623513 scopus 로고
    • Biorthogonal bases of compactly supported wavelet
    • A. COHEN, I. DAUBECHIES, AND J. FEAUVEAU, Biorthogonal bases of compactly supported wavelet, Comm. Pure Appl. Math., 45 (1992), pp. 485-560.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 485-560
    • Cohen, A.1    Daubechies, I.2    Feauveau, J.3
  • 14
    • 1842484444 scopus 로고    scopus 로고
    • Stability of multiscale transformations
    • W. DAHMEN, Stability of multiscale transformations, J. Fourier Anal. Appl., 2 (1996), pp. 341-362.
    • (1996) J. Fourier Anal. Appl. , vol.2 , pp. 341-362
    • Dahmen, W.1
  • 15
    • 0010574196 scopus 로고    scopus 로고
    • Uniform a priori estimates for singularly perturbed elliptic equations in multi-dimensions
    • W. DÖRFLER, Uniform a priori estimates for singularly perturbed elliptic equations in multi-dimensions, SIAM J. Numer. Anal., 36 (1999), pp. 1878-1900.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1878-1900
    • Dörfler, W.1
  • 16
    • 0026835579 scopus 로고
    • Stabilized finite element methods: I. Application to the advective-diffusive model
    • L. P. FRANCA, S. L. FREY, AND T. J. R. HUGHES, Stabilized finite element methods: I. Application to the advective-diffusive model, Comput. Methods Appl. Mech. Engrg., 95 (1992), pp. 253-276.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.95 , pp. 253-276
    • Franca, L.P.1    Frey, S.L.2    Hughes, T.J.R.3
  • 17
    • 25744449571 scopus 로고    scopus 로고
    • Wavelet Characterizations of Anisotropic Besov Spaces
    • Politecnico di Torino
    • G. GARRIGÓS AND A. TABACCO, Wavelet Characterizations of Anisotropic Besov Spaces, Report 27, Dipartimento di Matematica, Politecnico di Torino, 1999.
    • (1999) Report 27, Dipartimento di Matematica
    • Garrigós, G.1    Tabacco, A.2
  • 18
  • 19
    • 45149144830 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations
    • T. J. R. HUGHES, L. P. FRANCA, AND G. M. HULBERT, A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg., 73 (1989), pp. 173-189.
    • (1989) Comput. Methods Appl. Mech. Engrg. , vol.73 , pp. 173-189
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.M.3
  • 23
    • 0003295738 scopus 로고
    • Theory of Function Spaces
    • Birkhäuser Verlag Basel-Boston-Stuttgart
    • H. TRIEBEL, Theory of Function Spaces, Monographs in Mathematics 78, Birkhäuser Verlag Basel-Boston-Stuttgart, 1983.
    • (1983) Monographs in Mathematics , vol.78
    • Triebel, H.1
  • 24
    • 0042467393 scopus 로고    scopus 로고
    • personal communication
    • H. TRIEBEL, personal communication, 1999.
    • (1999)
    • Triebel, H.1
  • 26
    • 0001007482 scopus 로고
    • A note on interpolation spaces
    • Harmonic Analysis, F. Ricci and G. Weiss, eds., Springer-Verlag, Berlin, Heidelberg, New York
    • T. WOLFF, A note on interpolation spaces, in Harmonic Analysis, F. Ricci and G. Weiss, eds., Lectures Notes in Math. 908, Springer-Verlag, Berlin, Heidelberg, New York, 1982, pp. 199-204.
    • (1982) Lectures Notes in Math. 908 , pp. 199-204
    • Wolff, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.