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Volumn 8, Issue 3, 2001, Pages 191-205

Strengthened Cauchy-Bunyakowski-Schwarz inequality for a three-dimensional elasticity system

Author keywords

3D elasticity; A posteriori error estimation; Finite element methods; Hierarchical methods; Multilevel methods; Preconditioning

Indexed keywords


EID: 0035579924     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1506(200104/05)8:3<191::AID-NLA229>3.0.CO;2-7     Document Type: Article
Times cited : (24)

References (24)
  • 1
    • 0003983867 scopus 로고
    • Analysis of a two-level scheme for solving finite element equations
    • Center for Numerical Analysis, University of Texas, Austin, TX
    • Bank R, Dupont T. Analysis of a two-level scheme for solving finite element equations. Technical Report CNA-159, Center for Numerical Analysis, University of Texas, Austin, TX, 1980.
    • (1980) Technical Report CNA-159
    • Bank, R.1    Dupont, T.2
  • 2
    • 0039836804 scopus 로고
    • On multigrid methods of the two-level type
    • Multigrid Methods, Proceedings, Köln-Porz, Hackbusch W, Trottenberg U. (eds)
    • Axelsson O. On multigrid methods of the two-level type, in Multigrid Methods, Proceedings, Köln-Porz, Hackbusch W, Trottenberg U. (eds), Lecture Notes in Mathematics, vol. 960, 1982; 352-367.
    • (1982) Lecture Notes in Mathematics , vol.960 , pp. 352-367
    • Axelsson, O.1
  • 3
    • 84966225868 scopus 로고
    • Preconditioning and two-level multigrid methods of arbitrary degree of approximation
    • Axelsson O, Gustafsson I. Preconditioning and two-level multigrid methods of arbitrary degree of approximation. Mathematics of Computation 1983; 40:219-242.
    • (1983) Mathematics of Computation , vol.40 , pp. 219-242
    • Axelsson, O.1    Gustafsson, I.2
  • 4
    • 0012672225 scopus 로고
    • The condition number of a multigrid method for solving the Poisson equation
    • Braess D. The condition number of a multigrid method for solving the Poisson equation. Numerische Mathematik 1981; 37:387-404.
    • (1981) Numerische Mathematik , vol.37 , pp. 387-404
    • Braess, D.1
  • 5
    • 0040250128 scopus 로고
    • The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation
    • Multigrid Methods, Proceedings, Köln-Porz, 1981, Hackbusch W, Trottenberg U (eds)
    • Braess D. The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation. In Multigrid Methods, Proceedings, Köln-Porz, 1981, Hackbusch W, Trottenberg U (eds), Lecture Notes in Mathematics, vol. 960, 1982; 368-387.
    • (1982) Lecture Notes in Mathematics , vol.960 , pp. 368-387
    • Braess, D.1
  • 6
    • 0003787979 scopus 로고
    • The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems
    • Multigrid Methods. Proceedings, Köln-Porz, 1981, Hackbusch W, Trottenberg U. (eds)
    • Maitre JF, Musy F. The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems. In Multigrid Methods. Proceedings, Köln-Porz, 1981, Hackbusch W, Trottenberg U. (eds), Lecture Notes in Mathematics, vol. 960, 1982; 535-544.
    • (1982) Lecture Notes in Mathematics , vol.960 , pp. 535-544
    • Maitre, J.F.1    Musy, F.2
  • 7
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods I
    • Axelsson O, Vassilevski P. Algebraic multilevel preconditioning methods I. Numerische Mathematik 1989; 56:157-177.
    • (1989) Numerische Mathematik , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.2
  • 9
    • 0026219648 scopus 로고
    • The role of the strengthened Cauchy-Bunyakowski-Schwarz inequality in multilevel methods
    • Eijkhout V, Vassilevski P. The role of the strengthened Cauchy-Bunyakowski-Schwarz inequality in multilevel methods. SIAM Review 1991; 33:405-419.
    • (1991) SIAM Review , vol.33 , pp. 405-419
    • Eijkhout, V.1    Vassilevski, P.2
  • 10
    • 0002514884 scopus 로고
    • Fast adaptive composite grid (FAC) methods: Theory for the variational case
    • McCormick S. Fast adaptive composite grid (FAC) methods: Theory for the variational case. Computer Supplement 1984; 5:115-121.
    • (1984) Computer Supplement , vol.5 , pp. 115-121
    • McCormick, S.1
  • 12
    • 34250126304 scopus 로고
    • On the multilevel splitting of finite spaces
    • Yserentant H. On the multilevel splitting of finite spaces. Numerische Mathematik 1986; 49:379-412.
    • (1986) Numerische Mathematik , vol.49 , pp. 379-412
    • Yserentant, H.1
  • 14
    • 0012788594 scopus 로고
    • Nearly optimal iterative methods for solving finite element elliptic equations based on the multilevel splitting of the matrix
    • Institute for Scientific Computing, University of Wyoming, Laramie, WY
    • Vassilevski P. Nearly optimal iterative methods for solving finite element elliptic equations based on the multilevel splitting of the matrix. Technical Report 1989-1990, Institute for Scientific Computing, University of Wyoming, Laramie, WY, 1989.
    • (1989) Technical Report 1989-1990
    • Vassilevski, P.1
  • 15
    • 84985370889 scopus 로고
    • Upper bound of the constant in the strengthened CBS inequality for FEM 2D elasticity equations
    • Margenov SD. Upper bound of the constant in the strengthened CBS inequality for FEM 2D elasticity equations. Numerical Linear Algebra and its Applications 1994; 1(1):65-74.
    • (1994) Numerical Linear Algebra and Its Applications , vol.1 , Issue.1 , pp. 65-74
    • Margenov, S.D.1
  • 16
    • 21344474266 scopus 로고    scopus 로고
    • Estimate of the constant in two strengthened CBS Inequalities for FEM systems of 2D elasticity. Application to multilevel methods and a posteriori error estimators
    • Achchab B, Maitre JF. Estimate of the constant in two strengthened CBS Inequalities for FEM systems of 2D elasticity. Application to multilevel methods and a posteriori error estimators. Numerical Linear Algebra and its Applications 1996; 3(2):147-159.
    • (1996) Numerical Linear Algebra and Its Applications , vol.3 , Issue.2 , pp. 147-159
    • Achchab, B.1    Maitre, J.F.2
  • 17
    • 0033418114 scopus 로고    scopus 로고
    • Stabilization of algebraic multilevel iteration methods; additive methods
    • Axelsson O. Stabilization of algebraic multilevel iteration methods; additive methods. Numerical Algorithms 1999; 21:23-47.
    • (1999) Numerical Algorithms , vol.21 , pp. 23-47
    • Axelsson, O.1
  • 18
    • 0039523557 scopus 로고    scopus 로고
    • Some remarks on the constant in the strengthened CBS inequality: Estimate for hierarchical finite element discretization of elasticity problems
    • Jung M, Maitre JF. Some remarks on the constant in the strengthened CBS inequality: estimate for hierarchical finite element discretization of elasticity problems. Numerical Methods for Partial Differential Equations 1999; 15(4): 469-488.
    • (1999) Numerical Methods for Partial Differential Equations , vol.15 , Issue.4 , pp. 469-488
    • Jung, M.1    Maitre, J.F.2
  • 19
    • 0040040139 scopus 로고    scopus 로고
    • Estimations d'erreur a posteriori en éléments finis hiérarchique. Application aux éléments finis mixtes
    • Achchab B, Agouzal A, Baranger J, Maitre JF. Estimations d'erreur a posteriori en éléments finis hiérarchique. Application aux éléments finis mixtes. Numerische Mathematik 1998; 80:159-179.
    • (1998) Numerische Mathematik , vol.80 , pp. 159-179
    • Achchab, B.1    Agouzal, A.2    Baranger, J.3    Maitre, J.F.4
  • 20
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • Bank RE, Weiser A. Some a posteriori error estimators for elliptic partial differential equations. Mathematics of Computation 1985; 44:283-301.
    • (1985) Mathematics of Computation , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 21
    • 0027642848 scopus 로고
    • A posteriori error estimates based on hierarchical bases
    • Bank RE, Smith RK. A posteriori error estimates based on hierarchical bases. SIAM Journal on Numerical Analysis 1993; 30:921-935.
    • (1993) SIAM Journal on Numerical Analysis , vol.30 , pp. 921-935
    • Bank, R.E.1    Smith, R.K.2
  • 22
    • 0029487171 scopus 로고
    • Tetrahedral grid refinement
    • Bey J. Tetrahedral grid refinement. Computing 1995; 55:355-378.
    • (1995) Computing , vol.55 , pp. 355-378
    • Bey, J.1
  • 23
    • 0005507591 scopus 로고
    • Hierarchical basis preconditioners for second order elliptic problems in three dimensions
    • October Department of Applied Mathematics, University of Washington
    • Ong MEG. Hierarchical basis preconditioners for second order elliptic problems in three dimensions. Technical Report No 89-3, October 1989, Department of Applied Mathematics, University of Washington.
    • (1989) Technical Report No 89-3
    • Ong, M.E.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.