메뉴 건너뛰기




Volumn 83, Issue 2, 2010, Pages 174-195

On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method

Author keywords

Error bounds; Finite element method; Linear elasticity; Output; Smoothed finite element method

Indexed keywords

DISPLACEMENT FIELD; ERROR BOUND; ERROR BOUNDS; FINITE ELEMENT COMPUTATIONS; J INTEGRAL; LINEAR ELASTICITY; LINEAR ELASTICITY PROBLEMS; LINEAR OUTPUT; LOCAL DISPLACEMENT; LOCAL QUANTITIES; PRIMAL AND DUAL PROBLEMS; SMOOTHED FINITE ELEMENT METHOD; SUB-PROBLEMS; UPPER AND LOWER BOUNDS;

EID: 77954290072     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2825     Document Type: Article
Times cited : (13)

References (22)
  • 1
    • 0001585002 scopus 로고
    • Error estimate procedure in the finite element method and applications
    • Ladevèze P, Leguillon D. Error estimate procedure in the finite element method and applications. SIAM Journal on Numerical Analysis 1983; 20:485-509.
    • (1983) SIAM Journal On Numerical Analysis , vol.20 , pp. 485-509
    • Ladevèze, P.1    Leguillon, D.2
  • 2
    • 84966215690 scopus 로고
    • Some a posteriori error indicators for elliptic partial differential equations
    • Bank RE, Weiser A. Some a posteriori error indicators for elliptic partial differential equations. Mathematics of Computation 1985; 44:283-301.
    • (1985) Mathematics of Computation , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 4
    • 0038934341 scopus 로고    scopus 로고
    • Explicit error bounds in a conforming finite element method
    • Destuynder P, Métivet B. Explicit error bounds in a conforming finite element method. Mathematics of Computation 1999; 68:1379-1396.
    • (1999) Mathematics of Computation , vol.68 , pp. 1379-1396
    • Destuynder, P.1    Métivet, B.2
  • 5
    • 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
  • 6
    • 0002677869 scopus 로고    scopus 로고
    • Bounds for linear-functional outputs of coercive partial differential equations: Local indicators and adaptive refinement
    • Ladevéze P, Oden JT (eds). Elsevier: Amsterdam
    • Peraire J, Patera AT. Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement. Proceedings of the Workshop on New Advances in Adaptive Computational Methods in Mechanics. Ladevéze P, Oden JT (eds). Elsevier: Amsterdam, 1998.
    • (1998) Proceedings of The Workshop On New Advances In Adaptive Computational Methods In Mechanics
    • Peraire, J.1    Patera, A.T.2
  • 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
  • 8
    • 0034817636 scopus 로고    scopus 로고
    • Goal-oriented error estimation and adaptivity for the finite element method
    • Oden JT, Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method. Computers and Mathematics with Applications 2001; 41:735-756.
    • (2001) Computers and Mathematics With Applications , vol.41 , pp. 735-756
    • Oden, J.T.1    Prudhomme, S.2
  • 9
    • 27744567137 scopus 로고    scopus 로고
    • The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations
    • Parés N, Bonet J, Huerta A, Peraire J. The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations. Computer Methods in Applied Mechanics and Engineering 2006; 195:406-429.
    • (2006) Computer Methods In Applied Mechanics and Engineering , vol.195 , pp. 406-429
    • Parés, N.1    Bonet, J.2    Huerta, A.3    Peraire, J.4
  • 10
    • 0002646068 scopus 로고
    • Displacement and equilibrium models in finite element method
    • Zienkiewicz OC, Holister GS (eds). Wiley: Chichester
    • de Veubeke BF. Displacement and equilibrium models in finite element method. Stress Analysis. Zienkiewicz OC, Holister GS (eds). Wiley: Chichester, 1965; 145-197.
    • (1965) Stress Analysis , pp. 145-197
    • de Veubeke, B.F.1
  • 12
  • 13
    • 0027609952 scopus 로고
    • Finite element structural analysis and complementary energy
    • Gallagher RH. Finite element structural analysis and complementary energy. Finite Elements in Analysis and Design 1993; 13:115-126.
    • (1993) Finite Elements In Analysis and Design , vol.13 , pp. 115-126
    • Gallagher, R.H.1
  • 14
    • 55049084619 scopus 로고    scopus 로고
    • A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems
    • Liu GR, Zaw K, Wang YY, Deng B. A novel reduced-basis method with upper and lower bounds for real-time computation of linear elasticity problems. Computer Methods in Applied Mechanics and Engineering 2008; 198:269-279.
    • (2008) Computer Methods In Applied Mechanics and Engineering , vol.198 , pp. 269-279
    • Liu, G.R.1    Zaw, K.2    Wang, Y.Y.3    Deng, B.4
  • 15
    • 43749110663 scopus 로고    scopus 로고
    • Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM)
    • Liu GR, Zhang GY. Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM). International Journal for Numerical Methods in Engineering 2008; 74:1128-1161.
    • (2008) International Journal For Numerical Methods In Engineering , vol.74 , pp. 1128-1161
    • Liu, G.R.1    Zhang, G.Y.2
  • 16
    • 64449088696 scopus 로고    scopus 로고
    • A novel Galerkin-like weak form and superconvergent alpha finite element method for mechanics problems using triangle meshes
    • Liu GR, Nguyen-Xuan H, Nguyen-Thoi T, Xu X. A novel Galerkin-like weak form and superconvergent alpha finite element method for mechanics problems using triangle meshes. Journal of Computational Physics 2009; 228:4055-4087.
    • (2009) Journal of Computational Physics , vol.228 , pp. 4055-4087
    • Liu, G.R.1    Nguyen-Xuan, H.2    Nguyen-Thoi, T.3    Xu, X.4
  • 21
    • 34548675800 scopus 로고    scopus 로고
    • Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods
    • Chamoin L, Ladevèze LP. Bounds on history-dependent or independent local quantities in viscoelasticity problems solved by approximate methods. International Journal for Numerical Methods in Engineering 2007; 71: 1387-1411.
    • (2007) International Journal For Numerical Methods In Engineering , vol.71 , pp. 1387-1411
    • Chamoin, L.1    Ladevèze, L.P.2
  • 22
    • 0036945117 scopus 로고    scopus 로고
    • Matlab implementation of the finite element method in elasticity
    • Alberty J, Carstensen C, Funken SA, Klose R. Matlab implementation of the finite element method in elasticity. Computing 2002; 69:239-263.
    • (2002) Computing , vol.69 , pp. 239-263
    • Alberty, J.1    Carstensen, C.2    Funken, S.A.3    Klose, R.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.