메뉴 건너뛰기




Volumn 16, Issue 3, 2000, Pages 265-284

On the convergence of nonnested multigrid methods with nested spaces on coarse grids

Author keywords

Mixed finite elements; Multigrid methods; Nonconforming; Nonnested conforming; Second and fourth order problems; Uniform convergence

Indexed keywords


EID: 0005465292     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(200005)16:3<265::AID-NUM1>3.0.CO;2-8     Document Type: Article
Times cited : (3)

References (34)
  • 5
    • 0032623443 scopus 로고    scopus 로고
    • On the convergence of Galerkin-multigrid methods for nonconforming finite elements
    • Z. Chen, On the convergence of Galerkin-multigrid methods for nonconforming finite elements, East-West J Numer Math 7 (1999), 79-107.
    • (1999) East-West J Numer Math , vol.7 , pp. 79-107
    • Chen, Z.1
  • 6
    • 0032391964 scopus 로고    scopus 로고
    • Multigrid and multilevel methods for nonconforming rotated Q1 elements
    • Z. Chen and P. Oswald, Multigrid and multilevel methods for nonconforming rotated Q1 elements. Math Comp 67 (1998), 667-693.
    • (1998) Math Comp , vol.67 , pp. 667-693
    • Chen, Z.1    Oswald, P.2
  • 7
    • 0041741373 scopus 로고    scopus 로고
    • Convergence of multigrid methods for nonconforming finite elements without regularity assumptions
    • Z. Chen and D. Y. Kwak, Convergence of multigrid methods for nonconforming finite elements without regularity assumptions, Comp Appl Math 17 (1998), 283-302.
    • (1998) Comp Appl Math , vol.17 , pp. 283-302
    • Chen, Z.1    Kwak, D.Y.2
  • 8
    • 0029697285 scopus 로고    scopus 로고
    • Equivalence between and multigrid algorithms for mixed and nonconforming methods for second order elliptic problems
    • Z. Chen, Equivalence between and multigrid algorithms for mixed and nonconforming methods for second order elliptic problems, East-West J Numer Math 4 (1996), 1-33.
    • (1996) East-West J Numer Math , vol.4 , pp. 1-33
    • Chen, Z.1
  • 9
    • 0012375805 scopus 로고
    • A nonconforming multigrid method using conforming subspaces
    • N. Melson et al., eds., NASA Conference Publication 3224
    • C. Lee, A nonconforming multigrid method using conforming subspaces, Sixth Copper Mount Conf Multigrid Meth, N. Melson et al., eds., NASA Conference Publication 3224, Part 1, 1993, pp. 317-330.
    • (1993) Sixth Copper Mount Conf Multigrid Meth , Issue.1 PART , pp. 317-330
    • Lee, C.1
  • 10
    • 0040671516 scopus 로고
    • An application of the abstract multilevel theory to nonconforming finite element methods
    • P. S. Vassilevski and J. Wang, An application of the abstract multilevel theory to nonconforming finite element methods, SIAM J Numer Anal 32 (1995), 235-248.
    • (1995) SIAM J Numer Anal , vol.32 , pp. 235-248
    • Vassilevski, P.S.1    Wang, J.2
  • 11
    • 0039188959 scopus 로고
    • Convergence estimates for some multigrid algorithms
    • T. F. Chan, et al., Editors, SIAM, Philadelphia
    • J. Xu, Convergence estimates for some multigrid algorithms, T. F. Chan, et al., Editors, Decomposition methods for partial differential equations, SIAM, Philadelphia, 1990, pp. 174-187.
    • (1990) Decomposition Methods for Partial Differential Equations , pp. 174-187
    • Xu, J.1
  • 12
    • 0005445184 scopus 로고    scopus 로고
    • Multigrid algorithms for nonconforming and mixed methods for nonsymmetric and indefinite problems
    • Z. Chen, D. Y. Kwak, and Y. J. Yon, Multigrid algorithms for nonconforming and mixed methods for nonsymmetric and indefinite problems, SIAM J Sci Comp 19 (1998), 502-515.
    • (1998) SIAM J Sci Comp , vol.19 , pp. 502-515
    • Chen, Z.1    Kwak, D.Y.2    Yon, Y.J.3
  • 13
    • 84968500702 scopus 로고
    • On the implementation of mixed methods as nonconforming methods for second order elliptic problems
    • T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math Comp 64 (1995), 943-972.
    • (1995) Math Comp , vol.64 , pp. 943-972
    • Arbogast, T.1    Chen, Z.2
  • 14
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: Implementation, post-processing and error estimates
    • D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, post-processing and error estimates, RAIRO Model Math Anal Numer 19 (1985), 7-32.
    • (1985) RAIRO Model Math Anal Numer , vol.19 , pp. 7-32
    • Arnold, D.N.1    Brezzi, F.2
  • 15
    • 0002444350 scopus 로고
    • Analysis of mixed methods using conforming and nonconforming finite element methods
    • Z. Chen, Analysis of mixed methods using conforming and nonconforming finite element methods, RAIRO Math Model Numer Anal 21 (1993), 9-34.
    • (1993) RAIRO Math Model Numer Anal , vol.21 , pp. 9-34
    • Chen, Z.1
  • 16
    • 0030366993 scopus 로고    scopus 로고
    • Two-level additive Schwarz preconditioners for nonconforming finite elements
    • S. Brenner, Two-level additive Schwarz preconditioners for nonconforming finite elements. Math Comp 65 (1996), 897-921.
    • (1996) Math Comp , vol.65 , pp. 897-921
    • Brenner, S.1
  • 17
    • 0030372774 scopus 로고    scopus 로고
    • Preconditioners for nonconforming elements
    • P. Oswald, Preconditioners for nonconforming elements, Math Comp 65 (1996), 923-941.
    • (1996) Math Comp , vol.65 , pp. 923-941
    • Oswald, P.1
  • 19
    • 84968476488 scopus 로고
    • The analysis of smoothers for multigrid algorithms
    • J. Bramble and J. Pasciak, The analysis of smoothers for multigrid algorithms, Math Comp 58 (1992), 467-488.
    • (1992) Math Comp , vol.58 , pp. 467-488
    • Bramble, J.1    Pasciak, J.2
  • 20
    • 84966225317 scopus 로고
    • An optimal order process for solving finite element equations
    • R. Bank and T. Dupont, An optimal order process for solving finite element equations, Math Comp 36 (1981), 35-51.
    • (1981) Math Comp , vol.36 , pp. 35-51
    • Bank, R.1    Dupont, T.2
  • 21
    • 85037497695 scopus 로고    scopus 로고
    • Convergence of nonconforming multigrid methods without full elliptic regularity
    • to appear
    • S. Brenner, Convergence of nonconforming multigrid methods without full elliptic regularity, Math Comp, to appear.
    • Math Comp
    • Brenner, S.1
  • 22
    • 0039372108 scopus 로고
    • The W-cycle multigrid method for finite elements with nonnested spaces
    • M. Wang, The W-cycle multigrid method for finite elements with nonnested spaces, Adv in Math 23 (1994), 238-250.
    • (1994) Adv in Math , vol.23 , pp. 238-250
    • Wang, M.1
  • 23
    • 0040077938 scopus 로고
    • Approximation of coefficients in hybrid and mixed methods tor nonlinear parabolic problems
    • Z. Chen and J. Douglas, Jr., Approximation of coefficients in hybrid and mixed methods tor nonlinear parabolic problems, Mat Aplic Comp 10 (1991), 137-160.
    • (1991) Mat Aplic Comp , vol.10 , pp. 137-160
    • Chen, Z.1    Douglas J., Jr.2
  • 26
    • 0015762231 scopus 로고
    • Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
    • M. Crouzeix and P. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, RAIRO 3 (1973), 33-75.
    • (1973) RAIRO , vol.3 , pp. 33-75
    • Crouzeix, M.1    Raviart, P.2
  • 28
    • 38249001346 scopus 로고
    • Projection finite element methods for semiconductor device equations
    • Z. Chen, Projection finite element methods for semiconductor device equations, Comp Math App 25 (1993), 81-88.
    • (1993) Comp Math App , vol.25 , pp. 81-88
    • Chen, Z.1
  • 29
    • 0026837268 scopus 로고
    • Simple nonconforming quadrilateral Stokes element
    • R. Rannacher and S. Turek, Simple nonconforming quadrilateral Stokes element, Numer Meth Partial Diff Eq 8 (1992), 97-111.
    • (1992) Numer Meth Partial Diff Eq , vol.8 , pp. 97-111
    • Rannacher, R.1    Turek, S.2
  • 30
    • 0000650634 scopus 로고
    • The triangular equilibrium problem in the solution of plate bending problems
    • L. Morley, The triangular equilibrium problem in the solution of plate bending problems, Aero Quart 19 (1968), 149-169.
    • (1968) Aero Quart , vol.19 , pp. 149-169
    • Morley, L.1
  • 31
    • 84976757268 scopus 로고
    • Piecewise quadratic approximations on triangles
    • M. J. Powell and M. A. Sabin, Piecewise quadratic approximations on triangles, ACM Trans Mat Software 3 (1977), 316-325.
    • (1977) ACM Trans Mat Software , vol.3 , pp. 316-325
    • Powell, M.J.1    Sabin, M.A.2
  • 32
    • 0001558920 scopus 로고
    • The TUBA family of plate elements for the matrix displacement method
    • J. H. Argyris, I. Fried, and D. W. Scharps, The TUBA family of plate elements for the matrix displacement method. Aero J Roy Aero Soc 72 (1968), 701-709.
    • (1968) Aero J Roy Aero Soc , vol.72 , pp. 701-709
    • Argyris, J.H.1    Fried, I.2    Scharps, D.W.3
  • 33
    • 0040400135 scopus 로고
    • Analysis of plate bending by the finite element method
    • A. Adini and R. Clough, Analysis of plate bending by the finite element method, NSF Report G. 7337, 1961.
    • (1961) NSF Report G , vol.7337
    • Adini, A.1    Clough, R.2
  • 34
    • 0038552978 scopus 로고
    • The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas
    • Wright Patterson A.F.B., Ohio
    • F. K. Bogner, R. L. Fox, and L. A. Schmit, The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas, Proc Conf Matrix Meth Struc Mech. Wright Patterson A.F.B., Ohio, 1965.
    • (1965) Proc Conf Matrix Meth Struc Mech
    • Bogner, F.K.1    Fox, R.L.2    Schmit, L.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.