메뉴 건너뛰기




Volumn 84, Issue 13, 2010, Pages 1638-1664

Calculation of strict error bounds for finite element approximations of non-linear pointwise quantities of interest

Author keywords

Finite element method; Goal oriented error estimation; Handbook techniques; Non linear outputs; Strict bounds

Indexed keywords

ADJOINT PROBLEMS; ADJOINT SOLUTION; CONSTITUTIVE RELATION ERRORS; DISCRETIZATION ERRORS; DISPLACEMENT FIELD; ERROR BOUND; EXTRACTION TECHNIQUES; FATIGUE PROBLEMS; FINITE ELEMENT APPROXIMATIONS; GOAL-ORIENTED ERROR ESTIMATION; HIGHER ORDER; LOCAL ERROR BOUND; NON-LINEAR; PARTITION OF UNITY METHODS; PROJECTION PROPERTY; STRICT BOUNDS;

EID: 78649679229     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2957     Document Type: Article
Times cited : (47)

References (38)
  • 1
    • 0003602782 scopus 로고    scopus 로고
    • The Finite Element Method and its Reliability
    • Oxford University Press: Oxford,
    • Babuška I, Strouboulis T. The Finite Element Method and its Reliability. Oxford University Press: Oxford, 2001.
    • (2001)
    • Babuška, I.1    Strouboulis, T.2
  • 2
    • 18744380123 scopus 로고    scopus 로고
    • Error-controlled Adaptive Finite Elements in Solid Mechanics
    • Stein E (ed.). Wiley: New York,
    • Stein E (ed.). Error-controlled Adaptive Finite Elements in Solid Mechanics. Wiley: New York, 2003.
    • (2003)
  • 3
    • 18844373516 scopus 로고    scopus 로고
    • Mastering Calculations in Linear and Nonlinear Mechanics
    • Springer: NY,
    • Ladevèze P, Pelle J-P. Mastering Calculations in Linear and Nonlinear Mechanics. Springer: NY, 2004.
    • (2004)
    • Ladevèze, P.1    Pelle, J.2
  • 4
    • 0031443748 scopus 로고    scopus 로고
    • A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations
    • Paraschivoiu M, Peraire J, Patera AT. A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering 1997; 150:289-312.
    • (1997) Computer Methods in Applied Mechanics and Engineering , vol.150 , pp. 289-312
    • Paraschivoiu, M.1    Peraire, J.2    Patera, A.T.3
  • 7
    • 0032669875 scopus 로고    scopus 로고
    • On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors
    • Prudhomme S, Oden JT. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Computer Methods in Applied Mechanics and Engineering 1999; 176:313-331.
    • (1999) Computer Methods in Applied Mechanics and Engineering , vol.176 , pp. 313-331
    • Prudhomme, S.1    Oden, J.T.2
  • 9
    • 42449155099 scopus 로고    scopus 로고
    • Strict upper error bounds for calculated outputs of interest in computational structural mechanics
    • Ladevèze P. Strict upper error bounds for calculated outputs of interest in computational structural mechanics. Computational Mechanics 2008; 42(2):271-286.
    • (2008) Computational Mechanics , vol.42 , Issue.2 , pp. 271-286
    • Ladevèze, P.1
  • 10
    • 34548675800 scopus 로고    scopus 로고
    • Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods
    • Chamoin L, Ladevèze P. Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods. International Journal for Numerical Methods in Engineering 2007; 71(12):1387-1411.
    • (2007) International Journal for Numerical Methods in Engineering , vol.71 , Issue.12 , pp. 1387-1411
    • Chamoin, L.1    Ladevèze, P.2
  • 12
    • 74949087378 scopus 로고    scopus 로고
    • Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM
    • Panetier J, Ladevèze P, Chamoin L. Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM. International Journal for Numerical Methods in Engineering 2010; 81(6):671-700.
    • (2010) International Journal for Numerical Methods in Engineering , vol.81 , Issue.6 , pp. 671-700
    • Panetier, J.1    Ladevèze, P.2    Chamoin, L.3
  • 13
    • 36849058122 scopus 로고    scopus 로고
    • A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems
    • Chamoin L, Ladevèze P. A non-intrusive method for the calculation of strict and efficient bounds of calculated outputs of interest in linear viscoelasticity problems. Computer Methods in Applied Mechanics and Engineering 2008; 197(9-12):994-1014.
    • (2008) Computer Methods in Applied Mechanics and Engineering , vol.197 , Issue.9-12 , pp. 994-1014
    • Chamoin, L.1    Ladevèze, P.2
  • 14
    • 60949100350 scopus 로고    scopus 로고
    • Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems
    • Chamoin L, Ladevèze P. Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems. Finite Elements in Analysis and Design 2009; 45:251-262.
    • (2009) Finite Elements in Analysis and Design , vol.45 , pp. 251-262
    • Chamoin, L.1    Ladevèze, P.2
  • 16
    • 27744474569 scopus 로고    scopus 로고
    • Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems
    • Moitinho de Almeida JP, Almeida Pereira OJB. Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems. Computer Methods in Applied Mechanics and Engineering 2006; 195(4-6):279-296.
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , Issue.4-6 , pp. 279-296
    • Moitinho de Almeida, J.P.1    Almeida Pereira, O.J.B.2
  • 18
    • 73449133715 scopus 로고    scopus 로고
    • A new non-intrusive technique for the construction of admissible stress fields in model verification
    • Ladevèze P, Chamoin L, Florentin E. A new non-intrusive technique for the construction of admissible stress fields in model verification. Computer Methods in Applied Mechanics and Engineering 2010; 199(9-12):766-777.
    • (2010) Computer Methods in Applied Mechanics and Engineering , vol.199 , Issue.9-12 , pp. 766-777
    • Ladevèze, P.1    Chamoin, L.2    Florentin, E.3
  • 20
    • 0032046356 scopus 로고    scopus 로고
    • A new a posteriori error estimation for nonlinear time-dependent finite element analysis
    • Ladevèze P, Moës N. A new a posteriori error estimation for nonlinear time-dependent finite element analysis. Computer Methods in Applied Mechanics and Engineering 1998; 157:45-68.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.157 , pp. 45-68
    • Ladevèze, P.1    Moës, N.2
  • 21
    • 33746360900 scopus 로고    scopus 로고
    • Upper error bounds of calculated outputs of interest in linear and nonlinear structural mechanics
    • Ladevèze P. Upper error bounds of calculated outputs of interest in linear and nonlinear structural mechanics. Comptes Rendus Académie des Sciences Séries 2006; 334(7):399-407.
    • (2006) Comptes Rendus Académie des Sciences Séries , vol.334 , Issue.7 , pp. 399-407
    • Ladevèze, P.1
  • 24
    • 78649670788 scopus 로고
    • The post-processing approach in the finite element method, Part 2: the calculation of stress intensity factors
    • Babuška I, Miller A. The post-processing approach in the finite element method, Part 2: the calculation of stress intensity factors. Computer Methods in Applied Mechanics and Engineering 1987; 61:1-40.
    • (1987) Computer Methods in Applied Mechanics and Engineering , vol.61 , pp. 1-40
    • Babuška, I.1    Miller, A.2
  • 25
    • 0027553724 scopus 로고
    • Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control
    • Niu Q, Shephard MS. Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control. International Journal for Numerical Methods in Engineering 1993; 36:811-836.
    • (1993) International Journal for Numerical Methods in Engineering , vol.36 , pp. 811-836
    • Niu, Q.1    Shephard, M.S.2
  • 26
    • 0041322531 scopus 로고    scopus 로고
    • Pointwise and local error estimates for the quantities of interest in two-dimensional elasticity
    • Cao T, Kelly DW. Pointwise and local error estimates for the quantities of interest in two-dimensional elasticity. Computers and Mathematics with Applications 2003; 46(1):69-79.
    • (2003) Computers and Mathematics with Applications , vol.46 , Issue.1 , pp. 69-79
    • Cao, T.1    Kelly, D.W.2
  • 27
    • 36849129839 scopus 로고
    • Force at a point in the interior of a semi-infinite solid
    • Mindlin RD. Force at a point in the interior of a semi-infinite solid. Journal of Physics 1936; 7:195-202.
    • (1936) Journal of Physics , vol.7 , pp. 195-202
    • Mindlin, R.D.1
  • 28
    • 0003786889 scopus 로고
    • A Treatise on the Mathematical Theory of Elasticity
    • Dover: New York,
    • Love AEH. A Treatise on the Mathematical Theory of Elasticity. Dover: New York, 1944; 186-213.
    • (1944) , pp. 186-213
    • Love, A.E.H.1
  • 30
    • 20444440058 scopus 로고
    • Progress in Solid Mechanics
    • North Holland Publishing Company: Amsterdam,
    • Sneddon IN, Hill R. Progress in Solid Mechanics. North Holland Publishing Company: Amsterdam, 1964.
    • (1964)
    • Sneddon, I.N.1    Hill, R.2
  • 31
    • 0003472651 scopus 로고
    • Wave Motion in Elastic Solids
    • Dover Publications: New York,
    • Graff KF. Wave Motion in Elastic Solids. Dover Publications: New York, 1975.
    • (1975)
    • Graff, K.F.1
  • 32
    • 0023433462 scopus 로고
    • Green's functions for the biharmonic equation: bonded elastic media
    • Vijayakumar S, Cormack DE. Green's functions for the biharmonic equation: bonded elastic media. SIAM Journal on Applied Mathematics 1987; 47(5):982-997.
    • (1987) SIAM Journal on Applied Mathematics , vol.47 , Issue.5 , pp. 982-997
    • Vijayakumar, S.1    Cormack, D.E.2
  • 33
    • 0003458535 scopus 로고
    • Methods of Mathematical Physics
    • Interscience Publishers: New York,
    • Courant R, Hilbert D. Methods of Mathematical Physics. Interscience Publishers: New York, 1953.
    • (1953)
    • Courant, R.1    Hilbert, D.2
  • 37
    • 0033131520 scopus 로고    scopus 로고
    • A general formulation for a posteriori bounds for outputs functionals of partial differential equations; application to the eigenvalue problem
    • Maday Y, Patera A, Peraire J. A general formulation for a posteriori bounds for outputs functionals of partial differential equations; application to the eigenvalue problem. Comptes Rendus Académie des Sciences Séries 1999; 328:823-828.
    • (1999) Comptes Rendus Académie des Sciences Séries , vol.328 , pp. 823-828
    • Maday, Y.1    Patera, A.2    Peraire, J.3
  • 38
    • 78649676365 scopus 로고    scopus 로고
    • Development of a post-processor for a posteriori error estimation of quantities of interest. Internal Report, Texas Institute for Computational and Applied Mathematics
    • Oden JT, Prudhomme S, Bass J, Westermann T. Development of a post-processor for a posteriori error estimation of quantities of interest. Internal Report, Texas Institute for Computational and Applied Mathematics, 2001.
    • (2001)
    • Oden, J.T.1    Prudhomme, S.2    Bass, J.3    Westermann, T.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.