메뉴 건너뛰기




Volumn 101, Issue 4, 2005, Pages 663-687

Finite element approximation of multi-scale elliptic problems using patches of elements

Author keywords

[No Author keywords available]

Indexed keywords


EID: 26644457920     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-005-0614-5     Document Type: Article
Times cited : (35)

References (46)
  • 1
    • 21344474266 scopus 로고    scopus 로고
    • Estimate of the constant in two strengthened C.B.S. inequalities for F.E.M. systems of 2D elasticiy: Application of multilevel methods and a posteriori error estimators
    • Achchab, B., Maître, J.-F.: Estimate of the constant in two strengthened C.B.S. inequalities for F.E.M. systems of 2D elasticiy: Application of multilevel methods and a posteriori error estimators. Numer. Linear Algebra Appl. 3(2), 147-159 (1996)
    • (1996) Numer. Linear Algebra Appl. , vol.3 , Issue.2 , pp. 147-159
    • Achchab, B.1    Maître, J.-F.2
  • 2
    • 0038693388 scopus 로고    scopus 로고
    • The mortar element method with overlapping subdomains
    • Achdou, Y., Maday, Y.: The mortar element method with overlapping subdomains. SIAM J. Numer. Anal. 40(2), 601-628 (2002)
    • (2002) SIAM J. Numer. Anal. , vol.40 , Issue.2 , pp. 601-628
    • Achdou, Y.1    Maday, Y.2
  • 4
    • 0039836804 scopus 로고
    • On multigrid methods of the two-level type
    • W. Hackbusch, U. Trottenberg (eds.), Multigrid Methods. Springer-Verlag, Berlin
    • Axelsson, O.: On multigrid methods of the two-level type. In: W. Hackbusch, U. Trottenberg (eds.), Multigrid Methods. Vol. 960 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1981 pp. 352-367
    • (1981) Lecture Notes in Mathematics , vol.960 , pp. 352-367
    • Axelsson, O.1
  • 5
    • 0033418114 scopus 로고    scopus 로고
    • Stabilization of algebraic multilevel iteration methods; additive methods
    • Axelsson, O.: Stabilization of algebraic multilevel iteration methods; additive methods. Numer. Algorithms 21, 23-47 (1999)
    • (1999) Numer. Algorithms , vol.21 , pp. 23-47
    • Axelsson, O.1
  • 7
    • 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. Math. Comp. 40(161), 219-242 (1983)
    • (1983) Math. Comp. , vol.40 , Issue.161 , pp. 219-242
    • Axelsson, O.1    Gustafsson, I.2
  • 8
    • 0000779223 scopus 로고
    • Algebraic multilevel preconditioning methods
    • Axelsson, O., Vassilevski, P.S.: Algebraic multilevel preconditioning methods. I. Numer. Math. 56, 157-177 (1989)
    • (1989) I. Numer. Math. , vol.56 , pp. 157-177
    • Axelsson, O.1    Vassilevski, P.S.2
  • 9
    • 0001573921 scopus 로고
    • Algebraic multilevel preconditioning methods. II
    • Axelsson, O., Vassilevski, P.S.: Algebraic multilevel preconditioning methods. II. SIAM J. Numer. Anal. 27(6), 1569-1590 (1990)
    • (1990) SIAM J. Numer. Anal. , vol.27 , Issue.6 , pp. 1569-1590
    • Axelsson, O.1    Vassilevski, P.S.2
  • 10
    • 0001377512 scopus 로고
    • The hierarchical basis multigrid method
    • Bank, R.E., Dupont, T.F., Yserentant, H.: The hierarchical basis multigrid method. Numer. Math. 52, 427-458 (1988)
    • (1988) Numer. Math. , vol.52 , pp. 427-458
    • Bank, R.E.1    Dupont, T.F.2    Yserentant, H.3
  • 11
    • 0027642848 scopus 로고
    • A posteriori error estimates based on hierarchical bases
    • Bank, R.E., Smith, R.K.: A posteriori error estimates based on hierarchical bases. SIAM J. Numer. Anal.30(4), 921-935 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , Issue.4 , pp. 921-935
    • Bank, R.E.1    Smith, R.K.2
  • 12
    • 26644471595 scopus 로고    scopus 로고
    • Space decomposition preconditioners and parallel solvers
    • Prague. Springer-Verlag, to appear
    • Blaheta, R.: Space decomposition preconditioners and parallel solvers. In Conference Proceedings ENUMATH 2003, Prague. Springer-Verlag, to appear
    • Conference Proceedings ENUMATH 2003
    • Blaheta, R.1
  • 13
    • 0012672225 scopus 로고
    • The contraction number of a multigrid method for solving the poisson equation
    • Braess, D.: The Contraction Number of a Multigrid Method for Solving the Poisson Equation. Numer. Math. 37, 387-404 (1981)
    • (1981) Numer. Math. , vol.37 , pp. 387-404
    • Braess, D.1
  • 14
    • 0040250128 scopus 로고
    • The convergence rate of a multigrid method with gauss-seidel relaxation for the poisson equation
    • W. Hackbusch, U. Trottenberg(eds.), Multigrid Methods. Springer-Verlag, Berlin
    • Braess, D.: The Convergence Rate of a Multigrid Method with Gauss-Seidel Relaxation for the Poisson Equation. In: W. Hackbusch, U. Trottenberg(eds.), Multigrid Methods. Vol. 960 Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1981 pp. 368-386
    • (1981) Lecture Notes in Mathematics , vol.960 , pp. 368-386
    • Braess, D.1
  • 15
    • 0023984323 scopus 로고
    • A preconditioning technique for the efficient solution of problems with local grid refinement
    • Bramble, J.H., Ewing, R.E., Pasciak, J.E., Schatz, A.H.: A preconditioning technique for the efficient solution of problems with local grid refinement. Comput. Methods Appl. Mech. Engrg. 67, 149-159 (1988)
    • (1988) Comput. Methods Appl. Mech. Engrg. , vol.67 , pp. 149-159
    • Bramble, J.H.1    Ewing, R.E.2    Pasciak, J.E.3    Schatz, A.H.4
  • 16
    • 84966225192 scopus 로고
    • Convergence estimates for product iterative methods with applications to domain decomposition
    • Bramble, J.H., Pasciak, J.E., Wang, J., Xu, J.: Convergence estimates for product iterative methods with applications to domain decomposition. Math. Comp. 57(195), 1-21 (1991)
    • (1991) Math. Comp. , vol.57 , Issue.195 , pp. 1-21
    • Bramble, J.H.1    Pasciak, J.E.2    Wang, J.3    Xu, J.4
  • 18
    • 0027640852 scopus 로고
    • Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems
    • Cai, X.-C., Widlund, O.B.: Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems. SIAM J. Numer. Anal. 30(4), 936-952 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , Issue.4 , pp. 936-952
    • Cai, X.-C.1    Widlund, O.B.2
  • 19
    • 0030547401 scopus 로고    scopus 로고
    • Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids
    • Chan, T.F., Smith, B.F., Zou, J.: Overlapping Schwarz methods on unstructured meshes using non-matching coarse grids. Numer. Math. 73, 149-167 (1996)
    • (1996) Numer. Math. , vol.73 , pp. 149-167
    • Chan, T.F.1    Smith, B.F.2    Zou, J.3
  • 20
    • 0003470393 scopus 로고
    • Séminaire de Matheématiques Supérieures. Les Presses de L'Université de Montréal, Canada
    • Ciarlet, Ph.G.: Numerical Analysis of the Finite Element Method. Séminaire de Matheématiques Supérieures. Les Presses de L'Université de Montréal, Canada, 1976
    • (1976) Numerical Analysis of the Finite Element Method
    • Ciarlet, Ph.G.1
  • 21
    • 0026219648 scopus 로고
    • The role of the strengthened Cauchy-Buniakowskii-Schwarz inequality in multilevel methods
    • Eijkhout, V., Vassilevski, P.: The role of the strengthened Cauchy-Buniakowskii-Schwarz inequality in multilevel methods. SIAM Rev. 33(3), 405-419 (1991)
    • (1991) SIAM Rev. , vol.33 , Issue.3 , pp. 405-419
    • Eijkhout, V.1    Vassilevski, P.2
  • 22
    • 0346273552 scopus 로고    scopus 로고
    • Approximation of multi-scale elliptic problems using patches of finite elements
    • Glowinski, R., He, J., Rappaz, J., Wagner, J.: Approximation of multi-scale elliptic problems using patches of finite elements. C. R. Acad. Sci. Paris Ser. I 337, 679-684 (2003)
    • (2003) C. R. Acad. Sci. Paris Ser. I , vol.337 , pp. 679-684
    • Glowinski, R.1    He, J.2    Rappaz, J.3    Wagner, J.4
  • 23
    • 21844511143 scopus 로고
    • On the abstract theory of additive and multiplicative Schwarz algorithms
    • Griebel, M., Oswald, P.: On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math. 70, 163-180 (1995)
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 25
    • 0039523557 scopus 로고    scopus 로고
    • Some Remarks on the Constant in the Strengthened CBS Inequality: Estimate for hierarchical finite element discretizations of elasticity problems
    • Jung, M., Maître, J.-F.: Some Remarks on the Constant in the Strengthened CBS Inequality: Estimate for hierarchical finite element discretizations of elasticity problems. Numer. Methods Partial Differential Equations 15(4), 469-487 (1999)
    • (1999) Numer. Methods Partial Differential Equations , vol.15 , Issue.4 , pp. 469-487
    • Jung, M.1    Maître, J.-F.2
  • 26
    • 0038897091 scopus 로고    scopus 로고
    • Convergence d'un schéma itératif explicite
    • Laydi, M.R.: Convergence d'un schéma itératif explicite. C. R. Acad. Sci. Paris Ser. I 326, 511-514 (1998)
    • (1998) C. R. Acad. Sci. Paris Ser. I , vol.326 , pp. 511-514
    • Laydi, M.R.1
  • 27
    • 0003787979 scopus 로고
    • The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems
    • W. Hackbusch, U. Trottenberg (eds.), Multigrid Methods. Springer-Verlag
    • Berlin Maître, J.-F., Musy, F.: The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems. In: W. Hackbusch, U. Trottenberg (eds.), Multigrid Methods. Vol. 960 of Lecture Notes in Mathematics. Springer-Verlag, 1981, pp. 535-544
    • (1981) Lecture Notes in Mathematics , vol.960 , pp. 535-544
    • Berlin Maître, J.-F.1    Musy, F.2
  • 28
    • 84985370889 scopus 로고
    • Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations
    • Margenov, S.D.: Upper bound of the constant in the strengthened C.B.S. inequality for FEM 2D elasticity equations. Numer. Linear Algebra Appl. 1(1) 65-74 (1994)
    • (1994) Numer. Linear Algebra Appl. , vol.1 , Issue.1 , pp. 65-74
    • Margenov, S.D.1
  • 29
    • 0002514884 scopus 로고
    • Fast Adaptive Composite grid (FAC) Methods: Theory for the variational Case
    • K. B{ohner, H.J. Stetter (eds.), Defect Correction Methods. Theory and Applications. Springer
    • McCormick, S.F.: Fast Adaptive Composite grid (FAC) Methods: Theory for the variational Case. In: K. B{ohner, H.J. Stetter (eds.), Defect Correction Methods. Theory and Applications. Vol.5 of Computing Supplementum, Springer 1984, pp. 115-121
    • (1984) Computing Supplementum , vol.5 , pp. 115-121
    • McCormick, S.F.1
  • 30
    • 84966238687 scopus 로고
    • Unigrid formultigrid simulation
    • McCormick, S.F., Ruge,J.W.: Unigrid formultigrid simulation. Math. Comp. 41(163), 43-62 (1983)
    • (1983) Math. Comp. , vol.41 , Issue.163 , pp. 43-62
    • McCormick, S.F.1    Ruge, J.W.2
  • 31
    • 84966244637 scopus 로고
    • The Fast Adaptive Composite grid (FAC) method for elliptic equations
    • McCormick, S.F., Thomas, J.: The Fast Adaptive Composite Grid (FAC) Method for Elliptic Equations. Math. Comp. 46(174), 439-456 (1986)
    • (1986) Math. Comp. , vol.46 , Issue.174 , pp. 439-456
    • McCormick, S.F.1    Thomas, J.2
  • 33
    • 0000162763 scopus 로고
    • Ueber einen Grenzübergang durch alternirendes Verfahren
    • Chelsea Publishing Company, Bronx, New York
    • Schwarz, H.A.: Ueber einen Grenzübergang durch alternirendes Verfahren. Vol. 2 of Gesammelte Mathematische Abhandlungen. Chelsea Publishing Company, Bronx, New York, 1972, pp. 133-143
    • (1972) Gesammelte Mathematische Abhandlungen , vol.2 , pp. 133-143
    • Schwarz, H.A.1
  • 35
    • 0022797685 scopus 로고
    • On the use of composite grid schemes in computational aerodynamics
    • Steger, J.L., Benek, J.A.: On the use of composite grid schemes in computational aerodynamics. Comput. Methods Appl. Mech. Engrg. 64, 301-320 (1987)
    • (1987) Comput. Methods Appl. Mech. Engrg. , vol.64 , pp. 301-320
    • Steger, J.L.1    Benek, J.A.2
  • 36
    • 0027642364 scopus 로고
    • Convergence analysis of the Schwarz algorithm and multilevel decomposition iterative methods II: Nonselfadjoint and indefinite elliptic problems
    • Wang, J.: Convergence analysis of the Schwarz algorithm and multilevel decomposition iterative methods II: Nonselfadjoint and indefinite elliptic problems. SIAM J. Numer. Anal. 30(4), 953-970 (1993)
    • (1993) SIAM J. Numer. Anal. , vol.30 , Issue.4 , pp. 953-970
    • Wang, J.1
  • 37
    • 0037739577 scopus 로고    scopus 로고
    • Domain decomposition methods for elliptic partial differential equations
    • H. Bulgak, C. Zenger (eds.), Kluwer Academic Publishers
    • Widlund, O.B.: Domain decomposition methods for elliptic partial differential equations. In: H. Bulgak, C. Zenger (eds.), Error control and adaptativity in scientific computing. Kluwer Academic Publishers, 1999, pp. 325-354
    • (1999) Error Control and Adaptativity in Scientific Computing , pp. 325-354
    • Widlund, O.B.1
  • 38
    • 0003324460 scopus 로고
    • Discretization methods and iterative solvers based on domain decomposition
    • Springer
    • Wohlmuth, B.I.: Discretization methods and iterative solvers based on domain decomposition. Vol. 17 of Lecture Notes in Computational Science and Engineering. Springer, 1991
    • (1991) Lecture Notes in Computational Science and Engineering , vol.17
    • Wohlmuth, B.I.1
  • 39
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34(4), 581-613 (1992)
    • (1992) SIAM Rev. , vol.34 , Issue.4 , pp. 581-613
    • Xu, J.1
  • 41
    • 0035281551 scopus 로고    scopus 로고
    • The method of subspace corrections
    • Xu, J.: The method of subspace corrections. J. Comput. Appl. Math. 128, 335-362 (2001)
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 335-362
    • Xu, J.1
  • 44
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • Yserentant, H.: On the multi-level splitting of finite element spaces. Numer. Math. 49, 379-412 (1986)
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserentant, H.1
  • 46
    • 84971922635 scopus 로고
    • Old and new convergence proofs for multigrid methods
    • Yserentant, H.: Old and new convergence proofs for multigrid methods. Acta Numer. 285-326 (1993)
    • (1993) Acta Numer. , pp. 285-326
    • Yserentant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.