메뉴 건너뛰기




Volumn 195, Issue 4-6, 2006, Pages 207-213

The background of error estimation and adaptivity in finite element computations

Author keywords

Adaptive remeshing; Error estimation

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; STRAIN MEASUREMENT;

EID: 27744568797     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.07.053     Document Type: Article
Times cited : (44)

References (49)
  • 1
    • 0000170864 scopus 로고
    • The approximate arithmetical solution by finite differences of physical problems
    • L.F. Richardson The approximate arithmetical solution by finite differences of physical problems Trans. Roy. Soc. (London) A 210 1910 307-357
    • (1910) Trans. Roy. Soc. (London) A , vol.210 , pp. 307-357
    • Richardson, L.F.1
  • 2
    • 84985315731 scopus 로고
    • A-posteriori error estimates for the finite element method
    • I. Babuška C. Rheinboldt A-posteriori error estimates for the finite element method Int. J. Numer. Methods Engrg. 12 1978 1597-1615
    • (1978) Int. J. Numer. Methods Engrg. , vol.12 , pp. 1597-1615
    • Babuška, I.1    Rheinboldt, C.2
  • 3
    • 0017938585 scopus 로고
    • Adaptive approaches and reliability estimates in finite element analysis
    • I. Babuška C. Rheinboldt Adaptive approaches and reliability estimates in finite element analysis Comput. Methods Appl. Mech. Engrg. 17-18 1979 519-540
    • (1979) Comput. Methods Appl. Mech. Engrg. , vol.17-18 , pp. 519-540
    • Babuška, I.1    Rheinboldt, C.2
  • 4
    • 0026973251 scopus 로고
    • A procedure for a posteriori error estimation for h-p finite element methods
    • M. Ainsworth J.T. Oden A procedure for a posteriori error estimation for h-p finite element methods Comput. Methods Appl. Mech. Engrg. 101 1992 73-96
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 73-96
    • Ainsworth, M.1    Oden, J.T.2
  • 5
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using element residual methods
    • M. Ainsworth J.T. Oden A unified approach to a posteriori error estimation using element residual methods Numerische Mathematik 65 1993 23-50
    • (1993) Numerische Mathematik , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 6
    • 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 Engrg. 24 1987 337-357
    • (1987) Int. J. Numer. Methods Engrg. , vol.24 , pp. 337-357
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 7
    • 0015095659 scopus 로고
    • On the calculation of consistent stress distributions in finite element applications
    • H.J. Brauchli J.T. Oden On the calculation of consistent stress distributions in finite element applications Int. J. Numer. Methods Engrg. 3 1971 317-325
    • (1971) Int. J. Numer. Methods Engrg. , vol.3 , pp. 317-325
    • Brauchli, H.J.1    Oden, J.T.2
  • 8
    • 0026981573 scopus 로고
    • The superconvergent patch recovery (SPR) and adaptive finite element refinement
    • O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery (SPR) and adaptive finite element refinement Comput. Methods Appl. Mech. Engrg. 101 1992 207-224
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 207-224
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 9
    • 0026866050 scopus 로고
    • The superconvergent patch recovery (SPR) and a posteriori error estimates. Part 1: The recovery technique
    • O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery (SPR) and a posteriori error estimates. Part 1: The recovery technique Int. J. Numer. Methods Engrg. 33 1992 1331-1364
    • (1992) Int. J. Numer. Methods Engrg. , vol.33 , pp. 1331-1364
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 10
    • 0026869285 scopus 로고
    • The superconvergent patch recovery (SPR) and a posteriori error estimates. Part 2: Error estimates and adaptivity
    • O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery (SPR) and a posteriori error estimates. Part 2: Error estimates and adaptivity Int. J. Numer. Methods Engrg. 33 1992 1365-1382
    • (1992) Int. J. Numer. Methods Engrg. , vol.33 , pp. 1365-1382
    • Zienkiewicz, O.C.1    Zhu, J.Z.2
  • 12
    • 0027642884 scopus 로고
    • Patch recovery based on superconvergent derivatives and equilibrium
    • N.-E. Wiberg F. Abdulwahab Patch recovery based on superconvergent derivatives and equilibrium Int. J. Numer. Methods Engrg. 36 1993 2703-2724
    • (1993) Int. J. Numer. Methods Engrg. , vol.36 , pp. 2703-2724
    • Wiberg, N.-E.1    Abdulwahab, F.2
  • 13
    • 0028531773 scopus 로고
    • Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions
    • N.-E. Wiberg F. Abdulwahab S. Ziukas Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions Int. J. Numer. Methods Engrg. 37 1994 3417-3440
    • (1994) Int. J. Numer. Methods Engrg. , vol.37 , pp. 3417-3440
    • Wiberg, N.-E.1    Abdulwahab, F.2    Ziukas, S.3
  • 15
    • 3042983951 scopus 로고    scopus 로고
    • Error estimation and adaptive procedures based on superconvergent patch recovery (SPR)
    • N.-E. Wiberg F. Abdulwahab X.D. Li Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) Arch. Computat. Methods Engrg. 4 3 1997 203-242
    • (1997) Arch. Computat. Methods Engrg. , vol.4 , Issue.3 , pp. 203-242
    • Wiberg, N.-E.1    Abdulwahab, F.2    Li, X.D.3
  • 16
    • 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 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. Engrg. 114 1994 307-378
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.114 , pp. 307-378
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3
  • 18
    • 0041127816 scopus 로고
    • An objective criterion for assessing the reliability of a posteriori error estimators in finite element computations
    • I. Babuška T. Strouboulis C.S. Upadhyay S.K. Gangaraj K. Copps An objective criterion for assessing the reliability of a posteriori error estimators in finite element computations USACM Bull. 7 1994 4-16
    • (1994) USACM Bull. , vol.7 , pp. 4-16
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3    Gangaraj, S.K.4    Copps, K.5
  • 19
    • 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 K.S. Gangaraj A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method Int. J. Numer. Methods Engrg. 38 1995 4207-4235
    • (1995) Int. J. Numer. Methods Engrg. , vol.38 , pp. 4207-4235
    • Babuška, I.1    Strouboulis, T.2    Upadhyay, C.S.3    Gangaraj, K.S.4
  • 20
    • 0030871492 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 K.S. Gangaraj 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. Engrg. 140 1995 1-37
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.140 , pp. 1-37
    • Babuška, I.1    Strouboulis, T.2    Gangaraj, K.S.3    Upadhyay, C.S.4
  • 23
    • 0029408008 scopus 로고
    • Notes on mesh optimal criteria in adaptive finite element computations
    • L.Y. Li P. Bettess Notes on mesh optimal criteria in adaptive finite element computations Commun. Numer. Methods Engrg. 11 1995 911-915
    • (1995) Commun. Numer. Methods Engrg. , vol.11 , pp. 911-915
    • Li, L.Y.1    Bettess, P.2
  • 24
    • 0027643930 scopus 로고
    • A study of mesh optimality criteria in adaptive finite element analysis
    • E. Oñate G. Bugeda A study of mesh optimality criteria in adaptive finite element analysis Engrg. Computat. 10 1993 307-321
    • (1993) Engrg. Computat. , vol.10 , pp. 307-321
    • Oñate, E.1    Bugeda, G.2
  • 25
    • 0032628284 scopus 로고    scopus 로고
    • A unified approach to remeshing strategies for finite element h-adaptivity
    • P. Díez A. Huerta A unified approach to remeshing strategies for finite element h-adaptivity Comput. Methods Appl. Mech. Engrg. 176 1999 215-229
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.176 , pp. 215-229
    • Díez, P.1    Huerta, A.2
  • 26
    • 27744456701 scopus 로고    scopus 로고
    • Flux free residual a posteriori error estimators yielding simultaneous upper and lower bounds of the error
    • N.E. Wiberg, P. Díez, (Eds.), CIMNE, October
    • A. Huerta, N. Parés, P. Díez, Flux free residual a posteriori error estimators yielding simultaneous upper and lower bounds of the error, in: N.E. Wiberg, P. Díez, (Eds.), Adaptive Modeling and Simulation, vol. 1, CIMNE, October 2003, pp. 75-76.
    • (2003) Adaptive Modeling and Simulation , vol.1 , pp. 75-76
    • Huerta, A.1    Parés, N.2    Díez, P.3
  • 27
    • 27744494651 scopus 로고    scopus 로고
    • Local constitutive relation error for mises stresses in 3d elasticity
    • N.E. Wiberg, P. Díez, (Eds.), CIMNE, October
    • E. Florentin, L. Gallimard, P. Ladevèze, J.P. Pelle, P. Rougeot, Local constitutive relation error for mises stresses in 3d elasticity, in: N.E. Wiberg, P. Díez, (Eds.), Adaptive Modeling and Simulation, vol. 1, CIMNE, October 2003, pp. 73-74.
    • (2003) Adaptive Modeling and Simulation , vol.1 , pp. 73-74
    • Florentin, E.1    Gallimard, L.2    Ladevèze, P.3    Pelle, J.P.4    Rougeot, P.5
  • 28
    • 27744599889 scopus 로고    scopus 로고
    • Computing bounds for functional outputs of exact solutions of partial differential equations
    • N.E. Wiberg, P. Díez, (Eds.), CIMNE, October
    • J. Peraire, Computing bounds for functional outputs of exact solutions of partial differential equations, in: N.E. Wiberg, P. Díez, (Eds.), Adaptive Modeling and Simulation, vol. 1, CIMNE, October 2003, pp. 4-5.
    • (2003) Adaptive Modeling and Simulation , vol.1 , pp. 4-5
    • Peraire, J.1
  • 29
    • 27744593268 scopus 로고    scopus 로고
    • Guaranteed bounds for linear outputs of interest in elasticity
    • N.E. Wiberg, P. Díez, (Eds.), CIMNE, October
    • N. Parés, J. Bonet, A. Huerta, J. Peraire, Guaranteed bounds for linear outputs of interest in elasticity, in: N.E. Wiberg, P. Díez, (Eds.), Adaptive Modeling and Simulation, vol. 1, CIMNE, October 2003, pp. 78-79.
    • (2003) Adaptive Modeling and Simulation , vol.1 , pp. 78-79
    • Parés, N.1    Bonet, J.2    Huerta, A.3    Peraire, J.4
  • 30
    • 0002646068 scopus 로고
    • Displacement and equilibrium models in finite element method
    • O.C. Zienkiewicz G.S. Holister (Eds.) John Wiley and Sons Chichester
    • B. Fraeijs de Veubeke Displacement and equilibrium models in finite element method in: O.C. Zienkiewicz G.S. Holister (Eds.) Stress Analysis 1965 John Wiley and Sons Chichester 145-197
    • (1965) Stress Analysis , pp. 145-197
    • Fraeijs de Veubeke, B.1
  • 31
    • 0003390440 scopus 로고
    • Bending and stretching of plates. Special models for upper and lower bounds
    • AFFDL-TR-66-80, Wright Patterson Air force Base, Ohio, October
    • B. Fraeijs de Veubeke, Bending and stretching of plates. Special models for upper and lower bounds, in: Proc. First Conf. Matrix Methods in Structural Mechanics, vol. AFFDL-TR-66-80, Wright Patterson Air force Base, Ohio, October 1966, pp. 863-886.
    • (1966) Proc. First Conf. Matrix Methods in Structural Mechanics , pp. 863-886
    • Fraeijs de Veubeke, B.1
  • 32
    • 84965905157 scopus 로고
    • Strain energy bounds in finite element analysis by slab analogy
    • B. Fraeijs de Veubeke O.C. Zienkiewicz Strain energy bounds in finite element analysis by slab analogy J. Strain Anal. 2 1967 265-271
    • (1967) J. Strain Anal. , vol.2 , pp. 265-271
    • Fraeijs de Veubeke, B.1    Zienkiewicz, O.C.2
  • 33
    • 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 Engrg. 20 1984 1491-1506
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 1491-1506
    • Kelly, D.W.1
  • 34
    • 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 3 1983 485-509
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.3 , pp. 485-509
    • Ladevèze, P.1    Leguillon, D.2
  • 36
    • 84966215690 scopus 로고
    • Some a posteriori error estimators for elliptic partial differential equations
    • R.E. Bank A. Weiser Some a posteriori error estimators for elliptic partial differential equations Math. Computat. 44 1985 283-301
    • (1985) Math. Computat. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 38
    • 0021441740 scopus 로고
    • The post-processing approach in the finite element method. Part 1: Calculation of displacements, stresses and other higher derivatives of displacements
    • I. Babuška A. Miller The post-processing approach in the finite element method. Part 1: Calculation of displacements, stresses and other higher derivatives of displacements Int. J. Numer. Methods Engrg. 20 1984 1085-1109
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 1085-1109
    • Babuška, I.1    Miller, A.2
  • 39
    • 0021440959 scopus 로고
    • The post-processing approach in the finite element method. Part 2: The calculation of stress intensity factors
    • I. Babuška A. Miller The post-processing approach in the finite element method. Part 2: The calculation of stress intensity factors Int. J. Numer. Methods Engrg. 20 1984 1111-1129
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 1111-1129
    • Babuška, I.1    Miller, A.2
  • 40
    • 0021695793 scopus 로고
    • The post-processing approach in the finite element method. Part 3: A posteriori error estimates and adaptive mesh selection
    • I. Babuška A. Miller The post-processing approach in the finite element method. Part 3: A posteriori error estimates and adaptive mesh selection Int. J. Numer. Methods Engrg. 20 1984 2311-2324
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 2311-2324
    • Babuška, I.1    Miller, A.2
  • 41
    • 0031443748 scopus 로고    scopus 로고
    • A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
    • Symposium on Advances in Computational Mechanics, vol. 2 (Austin, TX, 1997)
    • M. Paraschivoiu, J. Peraire, A.T. Patera, A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations, Comput. Methods Appl. Mech. Engrg. 150(1-4):289-312 1997. Symposium on Advances in Computational Mechanics, vol. 2 (Austin, TX, 1997).
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.150 , Issue.1-4 , pp. 289-312
    • Paraschivoiu, M.1    Peraire, J.2    Patera, A.T.3
  • 42
    • 0032624694 scopus 로고    scopus 로고
    • Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations
    • J. Peraire A.T. Patera Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations Comput. Methods Appl. Mech. Engrg. 171 1-2 1999 77-86
    • (1999) Comput. Methods Appl. Mech. Engrg. , vol.171 , Issue.1-2 , pp. 77-86
    • Peraire, J.1    Patera, A.T.2
  • 43
    • 0035922230 scopus 로고    scopus 로고
    • A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem
    • L. Machiels J. Peraire A.T. Patera A posteriori finite-element output bounds for the incompressible Navier-Stokes equations: Application to a natural convection problem J. Computat. Phys. 172 2 2001 401-425
    • (2001) J. Computat. Phys. , vol.172 , Issue.2 , pp. 401-425
    • Machiels, L.1    Peraire, J.2    Patera, A.T.3
  • 44
    • 0033131520 scopus 로고    scopus 로고
    • A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem
    • Y. Maday A.T. Patera J. Peraire A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem C. R. Acad. Sci. Paris Sér. I Math. 328 9 1999 823-828
    • (1999) C. R. Acad. Sci. Paris Sér. I Math. , vol.328 , Issue.9 , pp. 823-828
    • Maday, Y.1    Patera, A.T.2    Peraire, J.3
  • 45
    • 27744442426 scopus 로고    scopus 로고
    • A general Lagrangian formulation for the computation of a posteriori finite element bounds
    • Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics Springer Berlin
    • A.T. Patera J. Peraire A general Lagrangian formulation for the computation of a posteriori finite element bounds in: Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics Lecture Notes Computer Science Engineering vol. 25 2003 Springer Berlin 159-206
    • (2003) Lecture Notes Computer Science Engineering , vol.25 , pp. 159-206
    • Patera, A.T.1    Peraire, J.2
  • 46
    • 0003216290 scopus 로고    scopus 로고
    • Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations
    • Industrial and Environmental Applications of Direct and Large-eddy Simulation (Istanbul 1998) Springer, Berlin
    • L. Machiels, J. Peraire, A.T. Patera, Output bound approximations for partial differential equations; application to the incompressible Navier-Stokes equations, in: Industrial and Environmental Applications of Direct and Large-eddy Simulation (Istanbul 1998), Lecture Notes in Physics, vol. 529, Springer, Berlin, 1999, pp. 93-108.
    • (1999) Lecture Notes in Physics , vol.529 , pp. 93-108
    • Machiels, L.1    Peraire, J.2    Patera, A.T.3
  • 48
    • 0033639755 scopus 로고    scopus 로고
    • Error estimation including pollution assessment for nonlinear finite element analysis
    • A. Huerta P. Díez Error estimation including pollution assessment for nonlinear finite element analysis Comput. Methods Appl. Mech. Engrg. 181 2000 21-41
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.181 , pp. 21-41
    • Huerta, A.1    Díez, P.2
  • 49
    • 0037436460 scopus 로고    scopus 로고
    • Recovering lower bounds of the error postprocessing implicit residual a posteriori error estimates
    • P. Díez N. Parés A. Huerta Recovering lower bounds of the error postprocessing implicit residual a posteriori error estimates Int. J. Numer. Methods Engrg. 56 2003 1465-1488
    • (2003) Int. J. Numer. Methods Engrg. , vol.56 , pp. 1465-1488
    • Díez, P.1    Parés, N.2    Huerta, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.