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Volumn 40, Issue 14, 1997, Pages 2571-2577

A model study of the quality of a posteriori error estimators for finite element solutions of linear elliptic problems, with particular reference to the behavior near the boundary

Author keywords

A posteriori error estimation; Asymptotic quality; Computer based analysis; Effect of the boundary; Finite element method

Indexed keywords


EID: 3943068360     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (28)
  • 1
    • 0028407162 scopus 로고
    • A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles
    • I. Babuška, T. Strouboulis and C. S. Upadhyay, 'A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles', Comput. Methods Appl. Mech. Eng., 114, 307-378 (1994).
    • (1994) Comput. Methods Appl. Mech. Eng. , vol.114 , pp. 307-378
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3
  • 3
    • 0001722808 scopus 로고
    • A model study of element residual estimators for linear elliptic problems: The quality of the estimators in the interior of meshes of triangles and quadrilaterals
    • I. Babuška, T. Strouboulis, C. S. Upadhyay and S. K. Gangaraj, 'A model study of element residual estimators for linear elliptic problems: The quality of the estimators in the interior of meshes of triangles and quadrilaterals',Comput. Struct., 57, 1009-1028 (1995).
    • (1995) Comput. Struct. , vol.57 , pp. 1009-1028
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3    Gangaraj, S.K.4
  • 4
    • 0026866050 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimators. Part 1. the recovery technique
    • O. C. Zienkiewicz and J. Z. Zhu, "The superconvergent patch recovery and a posteriori error estimators. Part 1. The recovery technique', Int. j. numer. methods eng., 33, 1331-1364 (1992).
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 5
    • 0026869285 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimators. Part 2. Error estimates and adaptivity
    • O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery and a posteriori error estimators. Part 2. Error estimates and adaptivity', Int. j. numer. methods eng., 33, 1365-1382 (1992).
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 1365-1382
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 6
    • 0027553411 scopus 로고
    • Superconvergent recovery techniques, some further tests
    • O. C. Zienkiewicz, J. Z. Zhu and J. Wu, 'Superconvergent recovery techniques, some further tests',Commun. Appl. Sci. Eng., 9, 251-258 (1993).
    • (1993) Commun. Appl. Sci. Eng. , vol.9 , pp. 251-258
    • Zienkiewicz, O.C.1    Zhu, J.Z.2    Wu, J.3
  • 7
    • 0026981573 scopus 로고
    • The superconvergent patch recovery (SPR) and adaptive finite element refinement
    • O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery (SPR) and adaptive finite element refinement',Comput. Methods Appl. Mech. Eng., 101, 207-224 (1992).
    • (1992) Comput. Methods Appl. Mech. Eng. , vol.101 , pp. 207-224
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 8
    • 0023288565 scopus 로고
    • A simple error estimator and the adaptive procedure for practical engineering analysis
    • O. C. Zienkiewicz and J. Z. Zhu, 'A simple error estimator and the adaptive procedure for practical engineering analysis',Int. j. numer. methods eng., 24, 337-357 (1987).
    • (1987) Int. J. Numer. Methods Eng. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 9
    • 0027642884 scopus 로고
    • Patch recovery based on superconvergent derivatives and equilibrium. Part 2. Error estimates and adaptivity
    • N. E. Wiberg and F. Abdulwahab, 'Patch recovery based on superconvergent derivatives and equilibrium. Part 2. Error estimates and adaptivity',Int. j. numer. methods eng., 36, 2703-2724 (1993).
    • (1993) Int. J. Numer. Methods Eng. , vol.36 , pp. 2703-2724
    • Wiberg, N.E.1    Abdulwahab, F.2
  • 11
    • 0028531773 scopus 로고
    • Enhanced superconvergent patch recovery incorporation equilibrium and boundary conditions
    • N. E. Wiberg, F. Abdulwahab and S. Ziukas, 'Enhanced superconvergent patch recovery incorporation equilibrium and boundary conditions',Int. j. numer. methods eng., 37, 3417-3440 (1994).
    • (1994) Int. J. Numer. Methods Eng. , vol.37 , pp. 3417-3440
    • Wiberg, N.E.1    Abdulwahab, F.2    Ziukas, S.3
  • 12
    • 0028377262 scopus 로고
    • Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements
    • T. Blacker and T. Belytschko, 'Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements',Int. j. numer. methods eng., 37, 517-536 (1994).
    • (1994) Int. J. Numer. Methods Eng. , vol.37 , pp. 517-536
    • Blacker, T.1    Belytschko, T.2
  • 13
    • 0022047205 scopus 로고
    • A proposed standard set of problems to test finite element accuracy
    • R. H. MacNeal and R. L. Harder, 'A proposed standard set of problems to test finite element accuracy', J. Finite Elem. Anal. Des., 1, 3-20 (1985).
    • (1985) J. Finite Elem. Anal. Des. , vol.1 , pp. 3-20
    • MacNeal, R.H.1    Harder, R.L.2
  • 14
    • 0028548590 scopus 로고
    • Pollution-error in the h-version of the finite-element method and the local quality of a posteriori error estimators
    • I. Babuška, T. Strouboulis, A. Mathur and C. S. Upadhyay, 'Pollution-error in the h-version of the finite-element method and the local quality of a posteriori error estimators', Finite Elem. Anal. Des., 17, 237-321 (1994).
    • (1994) Finite Elem. Anal. Des. , vol.17 , pp. 237-321
    • Babuška, I.1    Strouboulis, T.2    Mathur, A.3    Upadhyay, C.S.4
  • 15
    • 0029504921 scopus 로고
    • A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method
    • I. Babuška, T. Strouboulis , C. S. Upadhyay and S. K. Gangaraj, 'A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method', Int. j. numer. methods eng., 38, 4207-4235 (1995).
    • (1995) Int. J. Numer. Methods Eng. , vol.38 , pp. 4207-4235
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3    Gangaraj, S.K.4
  • 16
    • 0030871492 scopus 로고    scopus 로고
    • Pollution error in the h-version of the finite element method and the local quality of the recovered derivatives
    • I. Babuška, T. Strouboulis, S. K. Gangaraj and C. S. Upadhyay, 'Pollution error in the h-version of the finite element method and the local quality of the recovered derivatives',Comput. Methods Appl. Mech. Eng., 140, 1-39 (1997).
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.140 , pp. 1-39
    • Babuška, I.1    Strouboulis, T.2    Gangaraj, S.K.3    Upadhyay, C.S.4
  • 17
    • 0003391218 scopus 로고
    • Some studies of simple error estimators, Part I - The Philosophy
    • J. Robinson, E. A. W. Maunder and A. C. A. Ramsay, 'Some studies of simple error estimators, Part I - The Philosophy',Finite Elem. News, Issue No. 4, 38-42 (1992).
    • (1992) Finite Elem. News , Issue.4 , pp. 38-42
    • Robinson, J.1    Maunder, E.A.W.2    Ramsay, A.C.A.3
  • 18
    • 0003342915 scopus 로고
    • Some studies of simple error estimators, Part II, Problem I - Convergence characteristics of the error estimators
    • J. Robinson, E. A. W. Maunder and A. C. A. Ramsay, 'Some studies of simple error estimators, Part II, Problem I - Convergence characteristics of the error estimators',Finite Elem. News, Issue No. 5, 36-41 (1992).
    • (1992) Finite Elem. News , Issue.5 , pp. 36-41
    • Robinson, J.1    Maunder, E.A.W.2    Ramsay, A.C.A.3
  • 19
    • 0029306064 scopus 로고
    • η%-superconvergence of finite element approximations in the interior of general meshes of triangles
    • I. Babuška, T. Strouboulis and C. S. Upadhyay, η%-superconvergence of finite element approximations in the interior of general meshes of triangles',Comput. Methods Appl. Mech. Eng., 122, 273-305 (1995).
    • (1995) Comput. Methods Appl. Mech. Eng. , vol.122 , pp. 273-305
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3
  • 20
    • 24444442599 scopus 로고
    • η%-superconvergence in the interior of locally refined meshes of quadrilaterals: Superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations
    • I. Babuška, T. Strouboulis, S. K. Gangaraj and C. S. Upadhyay, η%-superconvergence in the interior of locally refined meshes of quadrilaterals: Superconvergence of the gradient in finite element solutions of Laplace's and Poisson's equations',Appl. Numer. Math., 16, 3-49 (1994).
    • (1994) Appl. Numer. Math. , vol.16 , pp. 3-49
    • Babuška, I.1    Strouboulis, T.2    Gangaraj, S.K.3    Upadhyay, C.S.4
  • 21
    • 0000958140 scopus 로고    scopus 로고
    • Computer-based proof of the existence of superconvergence points in the finite element method. Superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's and the elasticity equations
    • I. Babuška, T. Strouboulis, C. S. Upadhyay and S. K. Gangaraj, 'Computer-based proof of the existence of superconvergence points in the finite element method. Superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's and the elasticity equations',Numer. Methods PDEs, 12, 347-392 (1996).
    • (1996) Numer. Methods PDEs , vol.12 , pp. 347-392
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3    Gangaraj, S.K.4
  • 22
    • 0001968761 scopus 로고
    • Validation of recipes for the recovery of stresses and derivatives by a computer-based approach
    • I. Babuška, T. Strouboulis, S. K. Gangaraj and C. S. Upadhyay, 'Validation of recipes for the recovery of stresses and derivatives by a computer-based approach',Math. Comput. Modelling, 20, 45-89 (1994).
    • (1994) Math. Comput. Modelling , vol.20 , pp. 45-89
    • Babuška, I.1    Strouboulis, T.2    Gangaraj, S.K.3    Upadhyay, C.S.4
  • 23
    • 0026973251 scopus 로고
    • A procedure for a posteriori error estimation for h-p finite element methods
    • M. Ainsworth and J. T. Oden, 'A procedure for a posteriori error estimation for h-p finite element methods', Comput. Methods Appl. Mech. Eng., 101, 73-96 (1992).
    • (1992) Comput. Methods Appl. Mech. Eng. , vol.101 , pp. 73-96
    • Ainsworth, M.1    Oden, J.T.2
  • 24
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using element residual methods
    • M. Ainsworth and J. T. Oden, 'A unified approach to a posteriori error estimation using element residual methods', Numer. Math., 65, 23-50 (1993).
    • (1993) Numer. Math. , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 26
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and applications
    • P. Ladeveze and D. Leguillon, 'Error estimate procedure in the finite element method and applications',SIAM J. Numer. Anal, 20, 485-509 (1983).
    • (1983) SIAM J. Numer. Anal , vol.20 , pp. 485-509
    • Ladeveze, P.1    Leguillon, D.2
  • 27
    • 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, 283-301 (1985).
    • (1985) Math. Comp. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 28
    • 0041126577 scopus 로고
    • Ph.D. Thesis, Laboratoire de Mecanique et Technologie, E. N. S de Cachan-C.N.R.S-Universite Paris 6, Cachan, France
    • P. Rougeot, 'Sur le controle de la qualite des maillages elements finis',Ph.D. Thesis, Laboratoire de Mecanique et Technologie, E. N. S de Cachan-C.N.R.S-Universite Paris 6, Cachan, France, 1989.
    • (1989) Sur le Controle de la Qualite des Maillages Elements Finis
    • Rougeot, P.1


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