메뉴 건너뛰기




Volumn 88, Issue 1, 2001, Pages 9-42

Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035585768     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005442     Document Type: Article
Times cited : (27)

References (50)
  • 1
    • 0000773206 scopus 로고
    • Methods of fictitious domains for a second order elliptic equation with natural boundary conditions
    • G.P. Astrakantsev, Methods of fictitious domains for a second order elliptic equation with natural boundary conditions. U.S.S.R. Comput. Math. Math. Phys. 18, 114-121 (1978)
    • (1978) U.S.S.R. Comput. Math. Math. Phys. , vol.18 , pp. 114-121
    • Astrakantsev, G.P.1
  • 2
    • 34250459417 scopus 로고
    • The finite element method with Lagrange multipliers
    • I. Babuška, The finite element method with Lagrange multipliers. Numer. Math. 20, 179-192 (1973)
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuška, I.1
  • 3
    • 0025886026 scopus 로고
    • The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuska-Brezzi condition
    • H.J.C. Barbosa, T.J.R. Hughes, The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuska-Brezzi condition. Comput. Methods Appl. Mech. Eng. 85, 109-128 (1991)
    • (1991) Comput. Methods Appl. Mech. Eng. , vol.85 , pp. 109-128
    • Barbosa, H.J.C.1    Hughes, T.J.R.2
  • 4
    • 0034375557 scopus 로고    scopus 로고
    • Wavelet stabilization of the Lagrange multiplier method
    • to appear
    • S. Bertoluzza, Wavelet stabilization of the Lagrange multiplier method, to appear in Numer. Math.
    • Numer. Math.
    • Bertoluzza, S.1
  • 5
    • 0000713962 scopus 로고    scopus 로고
    • A multigrid algorithm for the mortar finite element method
    • D. Braess, W. Dahmen, C. Wieners, A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37, 48-69 (1999)
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 48-69
    • Braess, D.1    Dahmen, W.2    Wieners, C.3
  • 6
    • 84966242349 scopus 로고
    • The Lagrange multiplier method for Dirichlet's problem
    • J.H. Bramble, The Lagrange multiplier method for Dirichlet's problem. Math. Comp. 37, 1-11 (1981)
    • (1981) Math. Comp. , vol.37 , pp. 1-11
    • Bramble, J.H.1
  • 8
    • 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. Comp. Harm. Anal. 6, 1-52 (1999)
    • (1999) Appl. Comp. Harm. Anal. , vol.6 , pp. 1-52
    • Canuto, C.1    Tabacco, A.2    Urban, K.3
  • 9
    • 2742585462 scopus 로고    scopus 로고
    • Adaptive wavelet algorithms for elliptic operator equations - Convergence Rates
    • IGPM Report # 165, October to appear
    • A. Cohen, W. Dahmen, R. DeVore, Adaptive wavelet algorithms for elliptic operator equations - Convergence Rates. IGPM Report # 165, October 1998, RWTH Aachen. Math. Comp. (to appear)
    • (1998) RWTH Aachen. Math. Comp.
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 11
    • 1842484444 scopus 로고    scopus 로고
    • Stability of multiscale transformations
    • W. Dahmen, Stability of multiscale transformations. J. Fourier Anal. Appl. 4, 341-362 (1996)
    • (1996) J. Fourier Anal. Appl. , vol.4 , pp. 341-362
    • Dahmen, W.1
  • 12
    • 85011480386 scopus 로고    scopus 로고
    • Wavelet and multiscale methods for operator equations
    • W. Dahmen, Wavelet and multiscale methods for operator equations. Acta Numerica 6, 55-228 (1997)
    • (1997) Acta Numerica , vol.6 , pp. 55-228
    • Dahmen, W.1
  • 13
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • W. Dahmen, A. Kunoth, Multilevel preconditioning. Numer. Math. 63, 315-344 (1992)
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 14
    • 0001787026 scopus 로고    scopus 로고
    • Biorthogonal spline-wavelets on the interval - Stability and moment conditions
    • W. Dahmen, A. Kunoth, K. Urban, Biorthogonal spline-wavelets on the interval - Stability and moment conditions. Appl. Comp. Harm. Anal. 6, 132-196 (1999)
    • (1999) Appl. Comp. Harm. Anal. , vol.6 , pp. 132-196
    • Dahmen, W.1    Kunoth, A.2    Urban, K.3
  • 15
    • 0027574359 scopus 로고
    • Using the refinement equation for evaluating integrals of wavelets
    • W. Dahmen, C.A. Micchelli, Using the refinement equation for evaluating integrals of wavelets. SIAM J. Numer. Anal. 30, 507-537 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 507-537
    • Dahmen, W.1    Micchelli, C.A.2
  • 16
    • 0033426280 scopus 로고    scopus 로고
    • Composite wavelet bases for operator equations
    • W. Dahmen, R. Schneider, Composite wavelet bases for operator equations. Math. Comp. 68, 1533-1567 (1999)
    • (1999) Math. Comp. , vol.68 , pp. 1533-1567
    • Dahmen, W.1    Schneider, R.2
  • 17
    • 0033233501 scopus 로고    scopus 로고
    • Wavelets on manifolds I: Construction and domain decomposition
    • W. Dahmen, R. Schneider, Wavelets on manifolds I: Construction and domain decomposition. SIAM J. Math. Anal. 31, 184-230 (1999)
    • (1999) SIAM J. Math. Anal. , vol.31 , pp. 184-230
    • Dahmen, W.1    Schneider, R.2
  • 18
    • 0000619262 scopus 로고    scopus 로고
    • Wavelets with complementary boundary conditions - Function spaces on the cube
    • W. Dahmen, R. Schneider, Wavelets with complementary boundary conditions - Function spaces on the cube. Results in Mathematics 34, 255-293 (1998)
    • (1998) Results in Mathematics , vol.34 , pp. 255-293
    • Dahmen, W.1    Schneider, R.2
  • 19
    • 0000930347 scopus 로고    scopus 로고
    • Element-by element construction of wavelets satisfying stability and moment conditions
    • W. Dahmen, R. Stevenson, Element-by element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal. 37, 319-352 (1999)
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 319-352
    • Dahmen, W.1    Stevenson, R.2
  • 20
    • 0001217594 scopus 로고
    • Error analysis of a fictitious domain method applied to a Dirichlet problem
    • R. Glowinski, V. Girault, Error analysis of a fictitious domain method applied to a Dirichlet problem. Japan J. Industr. Appl. Maths. 12, 487-514 (1995)
    • (1995) Japan J. Industr. Appl. Maths. , vol.12 , pp. 487-514
    • Glowinski, R.1    Girault, V.2
  • 21
    • 0028333573 scopus 로고
    • A fictitious domain method for Dirichlet problem and applications
    • R. Glowinski, T.-W. Pan, J. Periaux, A fictitious domain method for Dirichlet problem and applications. Comp. Meth. Appl. Mech. Engin. 111, 283-303 (1994)
    • (1994) Comp. Meth. Appl. Mech. Engin. , vol.111 , pp. 283-303
    • Glowinski, R.1    Pan, T.-W.2    Periaux, J.3
  • 23
    • 0001149281 scopus 로고
    • Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls
    • 2AN 25, 711-748 (1991)
    • (1991) 2AN , vol.25 , pp. 711-748
    • Gunzburger, M.D.1    Hou, L.S.2    Svobodny, Th.P.3
  • 25
    • 0040478220 scopus 로고
    • Ph. D. Thesis, Verlag Shaker, Aachen, Germany, January
    • A. Kunoth, Multilevel Preconditioning. Ph. D. Thesis, Verlag Shaker, Aachen, Germany, January 1994
    • (1994) Multilevel Preconditioning
    • Kunoth, A.1
  • 26
    • 0342771981 scopus 로고
    • Computing refinable integrals - Documentation of the program - Version 1.1
    • Texas A&M University, May
    • A. Kunoth, Computing refinable integrals - Documentation of the program - Version 1.1. Technical Report ISC-95-02-Math, Texas A&M University, May 1995
    • (1995) Technical Report ISC-95-02-Math
    • Kunoth, A.1
  • 30
    • 0000000523 scopus 로고
    • Boundary subspaces for the finite element methods with Lagrange multipliers
    • J. Pitkäranta, Boundary subspaces for the finite element methods with Lagrange multipliers. Numer. Math. 33, 273-289 (1979)
    • (1979) Numer. Math. , vol.33 , pp. 273-289
    • Pitkäranta, J.1
  • 31
    • 0029395278 scopus 로고
    • On some techniques for approximating boundary conditions in the finite element method
    • R. Stenberg, On some techniques for approximating boundary conditions in the finite element method. J. Comp. Appl. Maths. 63, 139-148 (1995)
    • (1995) J. Comp. Appl. Maths. , vol.63 , pp. 139-148
    • Stenberg, R.1
  • 33
  • 34
    • 0009449519 scopus 로고
    • Interpolation in Regular Distributed Points
    • Curtiss, J.H. (1935): Interpolation in Regular Distributed Points, Trans. Amer. Math. Soc. 38, 458-473
    • (1935) Trans. Amer. Math. Soc. , vol.38 , pp. 458-473
    • Curtiss, J.H.1
  • 35
    • 0009375222 scopus 로고
    • Necessary Conditions in the Theory of Interpolation in the Complex Domain
    • Curtiss, J.H. (1941): Necessary Conditions in the Theory of Interpolation in the Complex Domain. Ann. of Math. 42, 634-646
    • (1941) Ann. of Math. , vol.42 , pp. 634-646
    • Curtiss, J.H.1
  • 36
    • 84972539420 scopus 로고
    • Riemann Sums and the Fundamental Polynomials of Lagrange Interpolation
    • Curtiss, J.H. (1941): Riemann Sums and the Fundamental Polynomials of Lagrange Interpolation. Duke Math. J. 8, 525-532
    • (1941) Duke Math. J. , vol.8 , pp. 525-532
    • Curtiss, J.H.1
  • 38
    • 2742588686 scopus 로고
    • On Interpolation in Complex Domain
    • German, A.H. (1980) On Interpolation in Complex Domain (in Russian). Analysis Math. 6, 121-135
    • (1980) Analysis Math. , vol.6 , pp. 121-135
    • German, A.H.1
  • 39
    • 2742593060 scopus 로고
    • Extremalpunkte und konforme Abbildung
    • Menke, K. (1972): Extremalpunkte und konforme Abbildung. Math. Ann. 195, 292-308
    • (1972) Math. Ann. , vol.195 , pp. 292-308
    • Menke, K.1
  • 41
    • 2742554854 scopus 로고
    • Bestimmung von Näherungen für die konforme Abbildung mit Hilfe stationärer Punktsysteme
    • Menke, K. (1974): Bestimmung von Näherungen für die konforme Abbildung mit Hilfe stationärer Punktsysteme. Numer. Math. 22, 111-117
    • (1974) Numer. Math. , vol.22 , pp. 111-117
    • Menke, K.1
  • 42
    • 0000054521 scopus 로고
    • Konforme Abbildung und Fekete-Punkte
    • Pommerenke, Ch. (1965): Konforme Abbildung und Fekete-Punkte. Math. Z. 89, 422-438
    • (1965) Math. Z. , vol.89 , pp. 422-438
    • Pommerenke, Ch.1
  • 43
    • 33646890104 scopus 로고
    • Über die Verteilung der Fekete-Punkte
    • Pommerenke, Ch. (1967): Über die Verteilung der Fekete-Punkte. Math. Ann. 168, 111-127
    • (1967) Math. Ann. , vol.168 , pp. 111-127
    • Pommerenke, Ch.1
  • 44
    • 2742587628 scopus 로고
    • Über die Verteilung der Fekete-Punkte II
    • Pommerenke, Ch. (1969): Über die Verteilung der Fekete-Punkte II. Math. Ann. 179, 212-218
    • (1969) Math. Ann. , vol.179 , pp. 212-218
    • Pommerenke, Ch.1
  • 45
    • 0003282273 scopus 로고
    • Boundary Behaviour of Conformal Maps
    • Springer, Berlin Heidelberg New York
    • Pommerenke, Ch. (1992): Boundary Behaviour of Conformal Maps. Grundlehren der mathematischen Wissenschaften Bd. 299. Springer, Berlin Heidelberg New York
    • (1992) Grundlehren der Mathematischen Wissenschaften , vol.299
    • Pommerenke, Ch.1
  • 46
    • 0009426366 scopus 로고    scopus 로고
    • Convergence of Processes of Interpolation in a Complex Domain
    • Shatalina, A.V. (1995): Convergence of Processes of Interpolation in a Complex Domain. Math. Notes 57, 107-109; translation from Mat. Zametki 57, 146-149
    • (1995) Math. Notes , vol.57 , pp. 107-109
    • Shatalina, A.V.1
  • 47
    • 0009426366 scopus 로고    scopus 로고
    • translation from
    • Shatalina, A.V. (1995): Convergence of Processes of Interpolation in a Complex Domain. Math. Notes 57, 107-109; translation from Mat. Zametki 57, 146-149
    • Mat. Zametki , vol.57 , pp. 146-149
  • 48
    • 0009369235 scopus 로고
    • On the Almost Everwhere Divergence of Lagrange Interpolation (Complex and Trigonometric Cases)
    • Vertesi, P. (1982): On the Almost Everwhere Divergence of Lagrange Interpolation (Complex and Trigonometric Cases). Acta Math. Acad. Sci. Hungar. 39, 367-377
    • (1982) Acta Math. Acad. Sci. Hungar. , vol.39 , pp. 367-377
    • Vertesi, P.1
  • 49
  • 50
    • 0041924089 scopus 로고
    • Mean Convergence of Interpolation Polynomials in a Domain with Corners
    • Zhong, L. (1994): Mean Convergence of Interpolation Polynomials in a Domain with Corners. J. Approximation Theory 77, 139-152
    • (1994) J. Approximation Theory , vol.77 , pp. 139-152
    • Zhong, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.