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Volumn 23, Issue 1, 1997, Pages 97-117

Multilevel iterative solution and adaptive mesh refinement for mixed finite element discretizations

Author keywords

Adaptive grid refinement; Mixed finite element methods; Multilevel iterative techniques

Indexed keywords

ADAPTIVE SYSTEMS; BOUNDARY VALUE PROBLEMS; ERROR ANALYSIS; HIERARCHICAL SYSTEMS; ITERATIVE METHODS; STIFFNESS MATRIX; TRIANGULATION;

EID: 0031071105     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(96)00063-3     Document Type: Article
Times cited : (5)

References (38)
  • 2
    • 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, Math. Modelling Numer. Anal. 19 (1985) 7-35.
    • (1985) Math. Modelling Numer. Anal. , vol.19 , pp. 7-35
    • Arnold, D.N.1    Brezzi, F.2
  • 3
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736-754.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 4
    • 84985315731 scopus 로고
    • A posteriori error estimates for the finite element method
    • I. Babuška and W.C. Rheinboldt, A posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12 (1978) 1597-1615.
    • (1978) Internat. J. Numer. Methods Engrg. , vol.12 , pp. 1597-1615
    • Babuška, I.1    Rheinboldt, W.C.2
  • 6
    • 0002641609 scopus 로고
    • Refinement algorithm and data structures for regular local mesh refinement
    • R. Stepleman et al., eds., North-Holland, Amsterdam
    • R.E. Bank, A.H. Sherman and A. Weiser, Refinement algorithm and data structures for regular local mesh refinement, in: R. Stepleman et al., eds., Scientific Computing (North-Holland, Amsterdam, 1983) 3-17.
    • (1983) Scientific Computing , pp. 3-17
    • Bank, R.E.1    Sherman, A.H.2    Weiser, A.3
  • 7
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp. 44 (1985) 283-301.
    • (1985) Math. Comp. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 8
    • 0001701058 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic problems in two and three space dimensions
    • F. Bornemann, B. Erdmann and Kornhuber, A posteriori error estimates for elliptic problems in two and three space dimensions, SIAM J. Numer. Anal. 33 (1996) 455-476.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 455-476
    • Bornemann, F.1    Erdmann, B.2    Kornhuber3
  • 9
    • 21144473187 scopus 로고
    • A basic norm equivalence for the theory of multilevel methods
    • F. Bornemann and H. Yserentant, A basic norm equivalence for the theory of multilevel methods, Numer. Math. 64 (1993) 455-476.
    • (1993) Numer. Math. , vol.64 , pp. 455-476
    • Bornemann, F.1    Yserentant, H.2
  • 11
    • 0000518260 scopus 로고    scopus 로고
    • A posteriori error estimators for the Raviart-Thomas element
    • D. Braess and R. Verfüth, A posteriori error estimators for the Raviart-Thomas element, SIAM J. Numer. Anal. 33 (1996).
    • (1996) SIAM J. Numer. Anal. , vol.33
    • Braess, D.1    Verfüth, R.2
  • 12
    • 0026882466 scopus 로고
    • A multigrid algorithm for the lowest-order Raviart-Thomas mixed triangular finite element method
    • S. Brenner, A multigrid algorithm for the lowest-order Raviart-Thomas mixed triangular finite element method, SIAM J. Numer. Anal. 29 (1992) 647-678.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 647-678
    • Brenner, S.1
  • 14
    • 0040124266 scopus 로고
    • Multilevel iteration for mixed finite element systems with penalty
    • Z. Cai, C.I. Goldstein and J. Pasciak, Multilevel iteration for mixed finite element systems with penalty, SIAM J. Sci. Comput. 14 (1993) 1072-1088.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1072-1088
    • Cai, Z.1    Goldstein, C.I.2    Pasciak, J.3
  • 16
    • 0004582161 scopus 로고
    • Mixed finite element methods for second order elliptic problems
    • J. Douglas and J.E. Roberts, Mixed finite element methods for second order elliptic problems, Math. Appl. Comput. 1 (1982) 91-103.
    • (1982) Math. Appl. Comput. , vol.1 , pp. 91-103
    • Douglas, J.1    Roberts, J.E.2
  • 19
    • 0001708409 scopus 로고
    • Analysis of the Schwarz algorithm for mixed finite element methods
    • R.E. Ewing and J. Wang, Analysis of the Schwarz algorithm for mixed finite element methods, Math. Modelling Numer. Anal. 26 (1992) 739-756.
    • (1992) Math. Modelling Numer. Anal. , vol.26 , pp. 739-756
    • Ewing, R.E.1    Wang, J.2
  • 20
    • 0013079015 scopus 로고
    • Analysis of multilevel decomposition iterative methods for mixed finite element methods
    • R.E. Ewing and J. Wang, Analysis of multilevel decomposition iterative methods for mixed finite element methods, Math. Modelling Numer. Anal. 28 (1994) 377-398.
    • (1994) Math. Modelling Numer. Anal. , vol.28 , pp. 377-398
    • Ewing, R.E.1    Wang, J.2
  • 21
    • 0029706640 scopus 로고    scopus 로고
    • Multilevel preconditioned augmented lagrangian techniques for 2nd order mixed problems
    • R. Hiptmair, T. Schiekofer and B. Wohlmuth, Multilevel preconditioned augmented Lagrangian techniques for 2nd order mixed problems, Computing 57 (1996) 25-48.
    • (1996) Computing , vol.57 , pp. 25-48
    • Hiptmair, R.1    Schiekofer, T.2    Wohlmuth, B.3
  • 22
    • 0000257741 scopus 로고    scopus 로고
    • Adaptive multilevel techniques for mixed finite element discretizations of elliptic boundary value problems
    • to appear
    • R.H.W. Hoppe and B. Wohlmuth, Adaptive multilevel techniques for mixed finite element discretizations of elliptic boundary value problems, SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal.
    • Hoppe, R.H.W.1    Wohlmuth, B.2
  • 23
    • 0003391212 scopus 로고
    • Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
    • R.H.W. Hoppe and B. Wohlmuth, Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods, Appl. Math. 40 (1995) 227-248.
    • (1995) Appl. Math. , vol.40 , pp. 227-248
    • Hoppe, R.H.W.1    Wohlmuth, B.2
  • 24
    • 0042012642 scopus 로고    scopus 로고
    • A comparison of a posteriori error estimators for mixed finite element discretizations
    • submitted
    • R.H.W. Hoppe and B. Wohlmuth, A comparison of a posteriori error estimators for mixed finite element discretizations, Math. Comp., submitted.
    • Math. Comp.
    • Hoppe, R.H.W.1    Wohlmuth, B.2
  • 26
    • 0027004931 scopus 로고
    • Adaptive finite element methods in computational mechanics
    • C. Johnson and P. Hansbo, Adaptive finite element methods in computational mechanics, Comput. Meth. Appl. Mech. Engrg. 101 (1992) 143-181.
    • (1992) Comput. Meth. Appl. Mech. Engrg. , vol.101 , pp. 143-181
    • Johnson, C.1    Hansbo, P.2
  • 28
    • 0000704501 scopus 로고
    • Mixed and hybrid methods
    • P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis, North-Holland, Amsterdam
    • J. Roberts and J.M. Thomas, Mixed and hybrid methods, in: P.G. Ciarlet and J.L. Lions, eds., Finite Element Methods (Part 1), Handbook of Numerical Analysis, Vol. II (North-Holland, Amsterdam, 1989).
    • (1989) Finite Element Methods , vol.2 , Issue.1 PART
    • Roberts, J.1    Thomas, J.M.2
  • 29
    • 21144466078 scopus 로고
    • Multilevel iterative methods for mixed finite element discretizations of elliptic problems
    • P.S. Vassilevski and J. Wang, Multilevel iterative methods for mixed finite element discretizations of elliptic problems, Numer. Math. 63 (1992) 503-520.
    • (1992) Numer. Math. , vol.63 , pp. 503-520
    • Vassilevski, P.S.1    Wang, J.2
  • 30
    • 0028423814 scopus 로고
    • A posteriori error estimation and adaptive mesh-refinement techniques
    • R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques, J. Comput. Appl. Math. 50 (1994) 67-83.
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 67-83
    • Verfürth, R.1
  • 33
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev. 34 (1992) 581-613.
    • (1992) SIAM Rev. , vol.34 , pp. 581-613
    • Xu, J.1
  • 34
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • H. Yserentant, On the multi-level splitting of finite element spaces, Numer. Math. 49 (1986) 379-412.
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserentant, H.1
  • 35
    • 0041511594 scopus 로고
    • Hierarchical bases in the numerical solution of parabolic problems
    • P. Deuflhard et al., eds., Birkhäuser, Basel
    • H. Yserentant, Hierarchical bases in the numerical solution of parabolic problems, in: P. Deuflhard et al., eds., Proc. Meet. Large Scale Scientific Computing (Birkhäuser, Basel, 1987) 22-36.
    • (1987) Proc. Meet. Large Scale Scientific Computing , pp. 22-36
    • Yserentant, H.1
  • 36
    • 84971922635 scopus 로고
    • Old and new convergence proofs for multigrid methods
    • H. Yserentant, Old and new convergence proofs for multigrid methods, Acta Numerica 1 (1993) 285-326.
    • (1993) Acta Numerica , vol.1 , pp. 285-326
    • Yserentant, H.1
  • 37
    • 34249840453 scopus 로고
    • Multilevel Schwarz methods
    • X. Zhang, Multilevel Schwarz methods, Numer. Math. 63 (1992) 521-539.
    • (1992) Numer. Math. , vol.63 , pp. 521-539
    • Zhang, X.1
  • 38
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Meth. Engrg. 24 (1987) 337-357.
    • (1987) Internat. J. Numer. Meth. Engrg. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.