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Volumn 28, Issue 2, 2008, Pages 331-353

An a posteriori error estimator for the Lamé equation based on equilibrated fluxes

Author keywords

A posteriori error estimates; Equilibrated fluxes; Linear elasticity; Mixed finite elements

Indexed keywords

A-POSTERIORI ERROR ESTIMATES; ARGYRIS ELEMENT; CONFORMING ELEMENTS; HIGHER ORDER TERMS; LINEAR ELASTICITY; MIXED FINITE ELEMENTS; NUMERICAL TESTS; POSTERIORI ERROR ESTIMATOR;

EID: 41549109300     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drm008     Document Type: Article
Times cited : (46)

References (35)
  • 1
    • 0000924189 scopus 로고    scopus 로고
    • Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems
    • AINSWORTH, M. & BABUŠKA, I. (1998) Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal., 36, 331-353.
    • (1998) SIAM J. Numer. Anal , vol.36 , pp. 331-353
    • AINSWORTH, M.1    BABUŠKA, I.2
  • 2
    • 38248999181 scopus 로고
    • A posteriori error estimators for 2nd order elliptic systems II. An optimal order process for calculating self-equilibrated fluxes
    • AINSWORTH, M. & ODEN, J. (1993) A posteriori error estimators for 2nd order elliptic systems II. An optimal order process for calculating self-equilibrated fluxes. Comput. Math. Appl., 26, 75-87.
    • (1993) Comput. Math. Appl , vol.26 , pp. 75-87
    • AINSWORTH, M.1    ODEN, J.2
  • 4
    • 23944472172 scopus 로고    scopus 로고
    • Rectangular mixed finite elements for elasticity
    • ARNOLD, D. N. & AWANOU, G. (2005) Rectangular mixed finite elements for elasticity. Math. Models Methods Appl. Sci., 15, 1417-1429.
    • (2005) Math. Models Methods Appl. Sci , vol.15 , pp. 1417-1429
    • ARNOLD, D.N.1    AWANOU, G.2
  • 5
    • 0036768154 scopus 로고    scopus 로고
    • Mixed finite element methods for elasticity
    • ARNOLD, D. N. & WINTHER, R. (2002) Mixed finite element methods for elasticity. Numer. Math., 92, 401-419.
    • (2002) Numer. Math , vol.92 , pp. 401-419
    • ARNOLD, D.N.1    WINTHER, R.2
  • 6
    • 41849128322 scopus 로고    scopus 로고
    • Mixed finite elements for elasticity in the stress-displacement formulation
    • Current Trends in Scientific Computing Z. Chen, R. Glowinski, & K. Li eds, Providence, RI: American Mathematical Society, pp
    • ARNOLD, D. N. & WINTHER, R. (2003) Mixed finite elements for elasticity in the stress-displacement formulation. Current Trends in Scientific Computing (Z. Chen, R. Glowinski, & K. Li eds), vol. 329. Contemporary Mathematics. Providence, RI: American Mathematical Society, pp. 33-42.
    • (2003) Contemporary Mathematics , vol.329 , pp. 33-42
    • ARNOLD, D.N.1    WINTHER, R.2
  • 7
    • 0026909316 scopus 로고
    • Analysis of the efficiency of an a posteriori error estimator for linear triangular elements
    • BABUŠKA, I., DURAN, R. & RODRIGUEZ, R. (1992) Analysis of the efficiency of an a posteriori error estimator for linear triangular elements. SIAM J. Numer. Anal., 29, 947-964.
    • (1992) SIAM J. Numer. Anal , vol.29 , pp. 947-964
    • BABUŠKA, I.1    DURAN, R.2    RODRIGUEZ, R.3
  • 8
    • 0023306715 scopus 로고
    • A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
    • BABUŠKA, I. & MILLER, A. (1987) A feedback finite element method with a posteriori error estimation. I: the finite element method and some basic properties of the a posteriori error estimator. Comput. Methods Appl. Mech. Eng., 61, 1-40.
    • (1987) Comput. Methods Appl. Mech. Eng , vol.61 , pp. 1-40
    • BABUŠKA, I.1    MILLER, A.2
  • 9
    • 84985315731 scopus 로고
    • A posteriori error estimates for the finite element method
    • BABUŠKA, I. & RHEINBOLDT, W. (1978) A posteriori error estimates for the finite element method. Int. J. Numer. Methods Eng., 12, 1597-1615.
    • (1978) Int. J. Numer. Methods Eng , vol.12 , pp. 1597-1615
    • BABUŠKA, I.1    RHEINBOLDT, W.2
  • 11
    • 84966215690 scopus 로고
    • Some a posteriori error estimates for elliptic partial differential equations
    • BANK, R. & WEISER, A. (1985) Some a posteriori error estimates for elliptic partial differential equations. Math. Comput., 44, 283-301.
    • (1985) Math. Comput , vol.44 , pp. 283-301
    • BANK, R.1    WEISER, A.2
  • 12
    • 84966215690 scopus 로고
    • Some a-posteriori error estimators for elliptic partial differential equations
    • BANK, R. E. & WEISER, A. (1990) Some a-posteriori error estimators for elliptic partial differential equations. Math. Comput., 44, 283-301.
    • (1990) Math. Comput , vol.44 , pp. 283-301
    • BANK, R.E.1    WEISER, A.2
  • 13
    • 85022001969 scopus 로고    scopus 로고
    • An optimal control approach to a posteriori error estimation in finite element methods
    • A. Iserles ed, Cambridge: Cambridge University Press, pp
    • BECKER, R. & RANNACHER, R. (2001) An optimal control approach to a posteriori error estimation in finite element methods. Acta Numerica 2001 (A. Iserles ed.). Cambridge: Cambridge University Press, pp. 1-102.
    • (2001) Acta Numerica 2001 , pp. 1-102
    • BECKER, R.1    RANNACHER, R.2
  • 16
    • 0032479720 scopus 로고    scopus 로고
    • A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems
    • BRINK, U. & STEIN, E. (1998) A posteriori error estimation in large-strain elasticity using equilibrated local Neumann problems. Comput. Methods Appl. Mech. Eng., 161, 77-101.
    • (1998) Comput. Methods Appl. Mech. Eng , vol.161 , pp. 77-101
    • BRINK, U.1    STEIN, E.2
  • 17
    • 23944466384 scopus 로고    scopus 로고
    • A posteriori dual-mixed adaptive finite element error control for Lamé and Stokes equations
    • CARSTENSEN, C., CAUSIN, P. & SACCO, R. (2005) A posteriori dual-mixed adaptive finite element error control for Lamé and Stokes equations. Numer. Math., 101, 309-332.
    • (2005) Numer. Math , vol.101 , pp. 309-332
    • CARSTENSEN, C.1    CAUSIN, P.2    SACCO, R.3
  • 19
    • 0021482394 scopus 로고
    • The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method
    • KELLY, D. (1984) The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method. Int. J. Numer. Methods Eng., 20, 1491-1506.
    • (1984) Int. J. Numer. Methods Eng , vol.20 , pp. 1491-1506
    • KELLY, D.1
  • 20
    • 0024770054 scopus 로고
    • Procedures for residual equilibration and local error estimation in the finite element method
    • KELLY, D. & ISLES, J. (1989) Procedures for residual equilibration and local error estimation in the finite element method. Commun. Appl. Numer. Methods, 5, 497-505.
    • (1989) Commun. Appl. Numer. Methods , vol.5 , pp. 497-505
    • KELLY, D.1    ISLES, J.2
  • 22
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and applications
    • LADEVÈZE, P. & LEGUILLON, D. (1983) Error estimate procedure in the finite element method and applications. SIAM J. Numer. Anal., 20, 485-509.
    • (1983) SIAM J. Numer. Anal , vol.20 , pp. 485-509
    • LADEVÈZE, P.1    LEGUILLON, D.2
  • 23
    • 0026121855 scopus 로고
    • Error estimates and. mesh optimization for finite element computation
    • LADEVÈZE, P., PELLE, J. P. & ROUGEOT, P. (1991) Error estimates and. mesh optimization for finite element computation. Eng. Comput., 8, 69-80.
    • (1991) Eng. Comput , vol.8 , pp. 69-80
    • LADEVÈZE, P.1    PELLE, J.P.2    ROUGEOT, P.3
  • 24
    • 0031336961 scopus 로고    scopus 로고
    • New advances on a posteriori error on constitutive relation in f.e. analysis
    • LADEVÈZE, P. & ROUGEOT, P. (1997) New advances on a posteriori error on constitutive relation in f.e. analysis. Comput. Methods Appl. Mech. Eng., 150, 239-249.
    • (1997) Comput. Methods Appl. Mech. Eng , vol.150 , pp. 239-249
    • LADEVÈZE, P.1    ROUGEOT, P.2
  • 25
    • 25444526084 scopus 로고    scopus 로고
    • A local a posteriori error estimator based, on equilibrated fluxes
    • LUCE, R. & WOHLMUTH, B. (2004) A local a posteriori error estimator based, on equilibrated fluxes. SIAM J. Numer. Anal., 42, 1394-1414.
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 1394-1414
    • LUCE, R.1    WOHLMUTH, B.2
  • 26
    • 26044475071 scopus 로고    scopus 로고
    • Reliable methods for computer simulation: Error control and a posteriori error estimates
    • Amsterdam: Elsevier
    • NEITTAANMAÄKI, P. & REPIN, S. (2004) Reliable methods for computer simulation: error control and a posteriori error estimates. Studies in Mathematics and Its Applications, vol. 33. Amsterdam: Elsevier.
    • (2004) Studies in Mathematics and Its Applications , vol.33
    • NEITTAANMAÄKI, P.1    REPIN, S.2
  • 27
    • 0035841388 scopus 로고    scopus 로고
    • Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems
    • OHNIMUS, S., STEIN, E. & WALHORN, E. (2001) Local error estimates of FEM for displacements and stresses in linear elasticity by solving local Neumann problems. Int. J. Numer. Methods Eng., 52, 727-746.
    • (2001) Int. J. Numer. Methods Eng , vol.52 , pp. 727-746
    • OHNIMUS, S.1    STEIN, E.2    WALHORN, E.3
  • 28
    • 0031373496 scopus 로고    scopus 로고
    • Equilibrium method for postprocessing and error estimation in the finite element method
    • STEIN, E. & OHNIMUS, S. (1997) Equilibrium method for postprocessing and error estimation in the finite element method. Comput. Assist. Mech. Eng. Sci., 4, 645-666.
    • (1997) Comput. Assist. Mech. Eng. Sci , vol.4 , pp. 645-666
    • STEIN, E.1    OHNIMUS, S.2
  • 29
    • 0032624207 scopus 로고    scopus 로고
    • Anisotopic discretization- and model-error estimation in solid mechanics by local Neumann problems
    • STEIN, E. & OHNIMUS, S. (1999) Anisotopic discretization- and model-error estimation in solid mechanics by local Neumann problems. Comput. Methods Appl Mech. Eng., 176, 363-385.
    • (1999) Comput. Methods Appl Mech. Eng , vol.176 , pp. 363-385
    • STEIN, E.1    OHNIMUS, S.2
  • 30
    • 22444453913 scopus 로고    scopus 로고
    • Adaptive finite element discretization in elasticity and elastoplasticity by global and local error estimators using local Neumann-problems
    • STEIN, E., OHNIMUS, S. & WALHORN, E. (1999) Adaptive finite element discretization in elasticity and elastoplasticity by global and local error estimators using local Neumann-problems. Z. Angew. Math. Mech., 79, 147-150.
    • (1999) Z. Angew. Math. Mech , vol.79 , pp. 147-150
    • STEIN, E.1    OHNIMUS, S.2    WALHORN, E.3
  • 31
    • 0003435748 scopus 로고    scopus 로고
    • A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques
    • Chichester: Wiley-Teubner
    • VERFÜRTH, R. (1996) A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner Series Advances in Numerical Mathematics. Chichester: Wiley-Teubner.
    • (1996) Wiley-Teubner Series Advances in Numerical Mathematics
    • VERFÜRTH, R.1
  • 32
    • 0032686338 scopus 로고    scopus 로고
    • A review of a posteriori error estimation techniques for elasticity problems
    • VERFÜRTH, R. (1999) A review of a posteriori error estimation techniques for elasticity problems. Comput. Methods Appl. Mech. Eng., 176, 419-440.
    • (1999) Comput. Methods Appl. Mech. Eng , vol.176 , pp. 419-440
    • VERFÜRTH, R.1
  • 34
    • 0023981522 scopus 로고    scopus 로고
    • Adaptive techniques in the finite element method
    • ZHU, J. Z. & ZIENKIEWICZ, O. C. (1998) Adaptive techniques in the finite element method. Commun. Appl. Numer. Methods, 4, 197-204.
    • (1998) Commun. Appl. Numer. Methods , vol.4 , pp. 197-204
    • ZHU, J.Z.1    ZIENKIEWICZ, O.C.2
  • 35
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • ZIENKIEWICZ, O. C. & ZHU, J. Z. (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 24, 337-357.
    • (1987) Int. J. Numer. Methods Eng , vol.24 , pp. 337-357
    • ZIENKIEWICZ, O.C.1    ZHU, J.Z.2


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