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Volumn 50, Issue 1-4, 1999, Pages 305-321

A unified approach to a posteriori error estimation based on duality error majorants

Author keywords

A posteriori error estimates; Duality theory; Variational problems

Indexed keywords


EID: 0001565662     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(99)00081-6     Document Type: Article
Times cited : (34)

References (27)
  • 1
    • 0000815647 scopus 로고
    • A posteriori error estimation in the finite element method
    • M. Ainthworth, T. Oden, A posteriori error estimation in the finite element method, Numer. Math. 60 (1992) 429-463.
    • (1992) Numer. Math. , vol.60 , pp. 429-463
    • Ainthworth, M.1    Oden, T.2
  • 2
    • 0010797981 scopus 로고
    • Some aspects of the method of hypercircle applied to elliptic variational problems
    • B. Hubbard (Ed.), SYNSPADE 1970, Academic Press, New York
    • J.P. Aubin, H.G. Burchard, Some aspects of the method of hypercircle applied to elliptic variational problems, in: B. Hubbard (Ed.), Numerical Solutions of Partial Differential Equations-II, SYNSPADE 1970, Academic Press, New York, 1974.
    • (1974) Numerical Solutions of Partial Differential Equations-II
    • Aubin, J.P.1    Burchard, H.G.2
  • 3
    • 84985315731 scopus 로고
    • A-posteriori error estimates for the finite element method
    • I. Babuška, W.C. Rheinboldt, A-posteriori error estimates for the finite element method, Int. J. Numer. Methods Eng. 12 (1978) 1597-1615.
    • (1978) Int. J. Numer. Methods Eng. , vol.12 , pp. 1597-1615
    • Babuška, I.1    Rheinboldt, W.C.2
  • 4
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. Babuška, 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
  • 5
    • 0027542059 scopus 로고
    • The problem of the selection of an a posteriori error indicator based on smoothing techniques
    • I. Babuška, R. Rodriguez, The problem of the selection of an a posteriori error indicator based on smoothing techniques, Int. J. Numer. Methods Eng. 36 (1993) 539-567.
    • (1993) Int. J. Numer. Methods Eng. , vol.36 , pp. 539-567
    • Babuška, I.1    Rodriguez, R.2
  • 6
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • R.E. Bank, W. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput. 44 (1985) 283-301.
    • (1985) Math. Comput. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, W.2
  • 9
    • 0027004931 scopus 로고
    • Adaptive finite element methods in computational mechanics
    • C. Johnson, P. Hansbo, Adaptive finite element methods in computational mechanics, Comput. Methods Appl. Mech. Eng. 101 (1994) 487-508.
    • (1994) Comput. Methods Appl. Mech. Eng. , vol.101 , pp. 487-508
    • Johnson, C.1    Hansbo, P.2
  • 10
    • 0021482394 scopus 로고
    • The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method
    • D.W. Kelly, The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method, Int. J. Numer. Methods Eng. 20 (1984) 1491-1506.
    • (1984) Int. J. Numer. Methods Eng. , vol.20 , pp. 1491-1506
    • Kelly, D.W.1
  • 11
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and applications
    • P. Ladevèze, D. Leguillon, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal. 20 (1983) 485-509.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 485-509
    • Ladevèze, P.1    Leguillon, D.2
  • 15
    • 0030494614 scopus 로고    scopus 로고
    • Errors of finite element methods for perfectly elasto-plastic problems
    • S.I. Repin, Errors of finite element methods for perfectly elasto-plastic problems, Math. Models Methods Appl. Sci. 6 (1996) 587-604.
    • (1996) Math. Models Methods Appl. Sci. , vol.6 , pp. 587-604
    • Repin, S.I.1
  • 18
    • 0040124973 scopus 로고    scopus 로고
    • A posteriori error estimates for variational problems with strongly convex functionals
    • S.I. Repin, A posteriori error estimates for variational problems with strongly convex functionals, Probl. Math. Anal. 17 (1997) 199-226 (in Russian, translated in the Journal of Mathematical Sciences, 1998).
    • (1997) Probl. Math. Anal. , vol.17 , pp. 199-226
    • Repin, S.I.1
  • 19
    • 0346393084 scopus 로고    scopus 로고
    • in Russian, translated
    • S.I. Repin, A posteriori error estimates for variational problems with strongly convex functionals, Probl. Math. Anal. 17 (1997) 199-226 (in Russian, translated in the Journal of Mathematical Sciences, 1998).
    • (1998) Journal of Mathematical Sciences
  • 20
    • 0347653895 scopus 로고    scopus 로고
    • A posteriori error estimation for variational problems with uniformly convex functionals
    • in press
    • S.I. Repin, A posteriori error estimation for variational problems with uniformly convex functionals, Math. Comp., in press.
    • Math. Comp.
    • Repin, S.I.1
  • 21
    • 0038940950 scopus 로고    scopus 로고
    • A posteriori error estimates for approximate solutions of variational problems by duality theory
    • H. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinski, Y. Kuznetsov and J. Perianx (Ed.), Heidelberg, 25 September 1997- 3 October 1997, VSP to appear
    • S.I. Repin, A posteriori error estimates for approximate solutions of variational problems by duality theory, in: H. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinski, Y. Kuznetsov and J. Perianx (Ed.), ENUMATH 97 Proceedings of the Second European Conference on Numerical Mathamatics and Advanced Applications, Heidelberg, 25 September 1997- 3 October 1997, VSP 1999, to appear.
    • (1999) ENUMATH 97 Proceedings of the Second European Conference on Numerical Mathamatics and Advanced Applications
    • Repin, S.I.1
  • 22
    • 0345762110 scopus 로고    scopus 로고
    • A posteriori estimates of the accuracy of variational methods for problems with nonconvex functionals
    • Algebra and Analysis
    • S.I. Repin, A posteriori estimates of the accuracy of variational methods for problems with nonconvex functionals, Algebra and Analysis, St. Petersburg Math. J. 11 (2000) No. 4.
    • (2000) St. Petersburg Math. J. , vol.11 , Issue.4
    • Repin, S.I.1
  • 23
    • 0030406640 scopus 로고    scopus 로고
    • A posteriori error estimation for elasto-plastic problems based on duality theory
    • S.I. Repin, L.S. Xanthis, A posteriori error estimation for elasto-plastic problems based on duality theory, Comput. Methods Appl. Mech. Eng. 138 (1996) 317-339.
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.138 , pp. 317-339
    • Repin, S.I.1    Xanthis, L.S.2
  • 25
    • 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
  • 27
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • O.C. Zienkiewicz, J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Eng. 24 (1987) 337-357.
    • (1987) Int. J. Numer. Methods Eng. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.