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Volumn 195, Issue 13-16, 2006, Pages 1573-1593

The multiscale approach to error estimation and adaptivity

Author keywords

A posteriori error estimation; Advection diffusion reaction equation; Stabilized methods; Variational multiscale method

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFUSION; FINITE ELEMENT METHOD; FLOW OF FLUIDS; GREEN'S FUNCTION; OPTIMIZATION;

EID: 30944448269     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.029     Document Type: Article
Times cited : (35)

References (48)
  • 1
    • 0000815647 scopus 로고
    • A posteriori error estimators in the finite element method
    • M. Ainsworth A.W. Craig A posteriori error estimators in the finite element method Numer. Math. 60 1991 429-463
    • (1991) Numer. Math. , vol.60 , pp. 429-463
    • Ainsworth, M.1    Craig, A.W.2
  • 2
    • 0042255750 scopus 로고
    • A unified approach to a posterior error estimation using element residual methods
    • M. Ainsworth J.T. Oden A unified approach to a posterior error estimation using element residual methods Numer. Math. 65 1993 23-50
    • (1993) Numer. Math. , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 5
    • 0023306715 scopus 로고
    • A feedback finite element method with a posteriori error estimation Part I. The finite element method and some basic properties of the a posteriori error estimator
    • I.M. Babuška A. Miller A feedback finite element method with a posteriori error estimation Part I. The finite element method and some basic properties of the a posteriori error estimator Comput. Methods Appl. Mech. Engrg. 61 1987 1-40
    • (1987) Comput. Methods Appl. Mech. Engrg. , vol.61 , pp. 1-40
    • Babuška, I.M.1    Miller, A.2
  • 6
    • 84985315731 scopus 로고
    • A posteriori error estimates for the finite element method
    • I.M. Babuška W.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.M.1    Rheinboldt, W.C.2
  • 7
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I.M. Babuška W.C. Rheinboldt Error estimates for adaptive finite element computations SIAM J. Numer. Anal. 18 1978 736-754
    • (1978) SIAM J. Numer. Anal. , vol.18 , pp. 736-754
    • Babuška, I.M.1    Rheinboldt, W.C.2
  • 8
    • 0017938585 scopus 로고
    • Adaptive approaches and reliability estimations in finite element analysis
    • I.M. Babuška W.C. Rheinboldt Adaptive approaches and reliability estimations in finite element analysis Comput. Methods Appl. Mech. Engrg. 17 1979 519-540
    • (1979) Comput. Methods Appl. Mech. Engrg. , vol.17 , pp. 519-540
    • Babuška, I.M.1    Rheinboldt, W.C.2
  • 10
    • 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. Comput. 44 1985 283-301
    • (1985) Math. Comput. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 13
    • 13344279006 scopus 로고
    • Adaptive mesh refinement techniques for aerodynamic problems
    • H. Alder J.C. Heinrich S. Lavanchy E. Oñate B. Suárez CIMNE Barcelona
    • G. Bugeda E. Oñate Adaptive mesh refinement techniques for aerodynamic problems H. Alder J.C. Heinrich S. Lavanchy E. Oñate B. Suárez Numerical Methods in Engineering and Applied Sciences 1992 CIMNE Barcelona
    • (1992) Numerical Methods in Engineering and Applied Sciences
    • Bugeda, G.1    Oñate, E.2
  • 14
    • 0032154265 scopus 로고    scopus 로고
    • A posteriori error estimation for standard finite element analysis
    • P. Diez A. Huerta A posteriori error estimation for standard finite element analysis Comput. Methods Appl. Mech. Engrg. 163 1998 141-157
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.163 , pp. 141-157
    • Diez, P.1    Huerta, A.2
  • 15
    • 84966225938 scopus 로고
    • An adaptive finite element method for linear elliptic problems
    • K. Eriksson C. Johnson An adaptive finite element method for linear elliptic problems Math. Comput. 50 1988 361-383
    • (1988) Math. Comput. , vol.50 , pp. 361-383
    • Eriksson, K.1    Johnson, C.2
  • 16
    • 0034351657 scopus 로고    scopus 로고
    • On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation
    • L.P. Franca F. Valentin On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation Comput. Methods Appl. Mech. Engrg. 190 2000 1785-1800
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 1785-1800
    • Franca, L.P.1    Valentin, F.2
  • 17
    • 0026835579 scopus 로고
    • Stabilized finite element methods: I. Application to the advective-diffusive model
    • L.P. Franca S.L. Frey T.J.R. Hughes Stabilized finite element methods: I. Application to the advective-diffusive model Comput. Methods Appl. Mech. Engrg. 95 1992 253-276
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.95 , pp. 253-276
    • Franca, L.P.1    Frey, S.L.2    Hughes, T.J.R.3
  • 18
    • 30944433029 scopus 로고    scopus 로고
    • The personal pre/postprocessing system
    • GiD CIMNE, Barcelona, www.gidhome.com
    • GiD, The personal pre/postprocessing system, CIMNE, Barcelona, www.gidhome.com, 2003.
    • (2003)
  • 19
    • 0035955565 scopus 로고    scopus 로고
    • Variational subgrid scale formulations for the advection-diffusion-reaction equation
    • Erratum: 191 (2002) 3123-3124
    • G. Hauke A. Garcia-Olivares Variational subgrid scale formulations for the advection-diffusion-reaction equation Comput. Methods Appl. Mech. Engrg. 190 2001 6847-6865 Erratum: 191 (2002) 3123-3124
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 6847-6865
    • Hauke, G.1    Garcia-Olivares, A.2
  • 20
    • 0037177644 scopus 로고    scopus 로고
    • A simple stabilized method for the advection-diffusion-reaction equation
    • G. Hauke A simple stabilized method for the advection-diffusion-reaction equation Comput. Methods Appl. Mech. Engrg. 191 2002 2925-2947
    • (2002) Comput. Methods Appl. Mech. Engrg. , vol.191 , pp. 2925-2947
    • Hauke, G.1
  • 21
    • 0033639755 scopus 로고    scopus 로고
    • Error estimation including pollution assessment for nonlinear finite element analysis
    • A. Huerta P. Diez 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    Diez, P.2
  • 22
    • 30944458862 scopus 로고    scopus 로고
    • Personal communication, Albuquerque
    • T.J.R. Hughes, Personal communication, Albuquerque, 2003.
    • (2003)
    • Hughes, T.J.R.1
  • 24
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
    • T.J.R. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods Comput. Methods Appl. Mech. Engrg. 127 1995 387-401
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 26
    • 0032123486 scopus 로고    scopus 로고
    • A posteriori error estimation of steady-state finite element solutions of the Navier-Stokes equations by a subdomain residual method
    • H. Jin S. Prudhomme A posteriori error estimation of steady-state finite element solutions of the Navier-Stokes equations by a subdomain residual method Comput. Methods Appl. Mech. Engrg. 159 1998 19-48
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.159 , pp. 19-48
    • Jin, H.1    Prudhomme, S.2
  • 27
    • 0034310682 scopus 로고    scopus 로고
    • A numerical study of a posteriori error estimators for convection-diffusion equations
    • V. John A numerical study of a posteriori error estimators for convection-diffusion equations Comput. Methods Appl. Mech. Engrg. 190 2000 757-781
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 757-781
    • John, V.1
  • 28
    • 0025488567 scopus 로고
    • Adaptive finite element methods for diffusion and convection problems
    • C. Johnson Adaptive finite element methods for diffusion and convection problems Comput. Methods Appl. Mech. Engrg. 82 1990 301-322
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.82 , pp. 301-322
    • Johnson, C.1
  • 29
    • 0009345560 scopus 로고
    • Finite element methods for flow problems
    • AGARD Report 787 AGARD, 7 Rue Ancelle, 92299 Neuilly sur Seine, France
    • C. Johnson, Finite element methods for flow problems, AGARD Report 787 AGARD, 7 Rue Ancelle, 92299 Neuilly sur Seine, France, 1992, 1-1-1-47.
    • (1992)
    • Johnson, C.1
  • 30
    • 0027004931 scopus 로고
    • Adaptive finite element methods in computational mechanics
    • C. Johnson P. Hansbo Adaptive finite element methods in computational mechanics Comput. Methods Appl. Mech. Engrg. 101 1992 143-181
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 143-181
    • Johnson, C.1    Hansbo, P.2
  • 31
    • 0020848572 scopus 로고
    • A posterior error analysis and adaptive processes in the finite element method. Part I - Error analysis
    • D.W. Kelly J.R. Gago O.C. Zienkiewicz I. Babuška A posterior error analysis and adaptive processes in the finite element method. Part I - Error analysis Int. J. Numer. Methods Engrg. 19 1983 1593-1610
    • (1983) Int. J. Numer. Methods Engrg. , vol.19 , pp. 1593-1610
    • Kelly, D.W.1    Gago, J.R.2    Zienkiewicz, O.C.3    Babuška, I.4
  • 32
    • 0025494150 scopus 로고
    • A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible Euler and Navier-Stokes equations
    • J.T. Oden L. Demkowicz W. Rachowicz T.A. Westermann A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible Euler and Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 82 1990 183-203
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.82 , pp. 183-203
    • Oden, J.T.1    Demkowicz, L.2    Rachowicz, W.3    Westermann, T.A.4
  • 33
    • 0027974409 scopus 로고
    • An a posterior error estimate for finite element approximations of the Navier-Stokes equations
    • J.T. Oden W. Wu M. Ainsworth An a posterior error estimate for finite element approximations of the Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 111 1994 185-202
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.111 , pp. 185-202
    • Oden, J.T.1    Wu, W.2    Ainsworth, M.3
  • 34
    • 27744481721 scopus 로고    scopus 로고
    • Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach
    • accepted for publication
    • E. Oñate, J. Arteaga, J. García, R. Flores, Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach, Comput. Methods Appl. Mech. Engrg., accepted for publication.
    • Comput. Methods Appl. Mech. Engrg.
    • Oñate, E.1    Arteaga, J.2    García, J.3    Flores, R.4
  • 35
    • 0034282854 scopus 로고    scopus 로고
    • A posteriori error estimators for stationary convection-diffusion problems: A computational comparison
    • A. Papastavrou R. Verfürth A posteriori error estimators for stationary convection-diffusion problems: A computational comparison Comput. Methods Appl. Mech. Engrg. 189 2000 449-462
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.189 , pp. 449-462
    • Papastavrou, A.1    Verfürth, R.2
  • 36
    • 0031443748 scopus 로고    scopus 로고
    • A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
    • 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 1997 289-312
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.150 , pp. 289-312
    • Paraschivoiu, M.1    Peraire, J.2    Patera, A.T.3
  • 37
    • 0030558903 scopus 로고    scopus 로고
    • A posteriori error estimators via bubble functions
    • A. Russo A posteriori error estimators via bubble functions Math. Models Methods Appl. Sci. 1 1996 33-41
    • (1996) Math. Models Methods Appl. Sci. , vol.1 , pp. 33-41
    • Russo, A.1
  • 38
    • 0031100781 scopus 로고    scopus 로고
    • An a posteriori error estimator and hp-adaptive strategy for finite element discretizations of the Helmholtz equation in exterior domains
    • J.R. Stewart T.J.R. Hughes An a posteriori error estimator and hp-adaptive strategy for finite element discretizations of the Helmholtz equation in exterior domains Finite Elem. Anal. Des. 25 1997 1-26
    • (1997) Finite Elem. Anal. Des. , vol.25 , pp. 1-26
    • Stewart, J.R.1    Hughes, T.J.R.2
  • 39
    • 0032072830 scopus 로고    scopus 로고
    • A tutorial in elementary finite element error analysis: A systematic presentation of a priori and a posteriori error estimates
    • J.R. Stewart T.J.R. Hughes A tutorial in elementary finite element error analysis: A systematic presentation of a priori and a posteriori error estimates Comput. Methods Appl. Mech. Engrg. 158 1998 1-22
    • (1998) Comput. Methods Appl. Mech. Engrg. , vol.158 , pp. 1-22
    • Stewart, J.R.1    Hughes, T.J.R.2
  • 40
    • 0025208435 scopus 로고
    • A posteriori error estimation of finite element approximations in fluid mechanics
    • T. Strouboulis J.T. Oden A posteriori error estimation of finite element approximations in fluid mechanics Comput. Methods Appl. Mech. Engrg. 78 1990 201-242
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.78 , pp. 201-242
    • Strouboulis, T.1    Oden, J.T.2
  • 41
    • 34249971216 scopus 로고
    • A posteriori error estimators for the Stokes problem
    • R. Verfürth A posteriori error estimators for the Stokes problem Numer. Math. 55 1989 309-325
    • (1989) Numer. Math. , vol.55 , pp. 309-325
    • Verfürth, R.1
  • 42
    • 0003435748 scopus 로고    scopus 로고
    • A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques
    • Wiley-Teuber
    • R. Verfürth A Review of a Posteriori Error Estimation and Adaptive Mesh-refinement Techniques 1996 Wiley-Teuber
    • (1996)
    • Verfürth, R.1
  • 43
    • 0038855305 scopus 로고    scopus 로고
    • A posteriori error estimators for convection-diffusion equations
    • R. Verfürth A posteriori error estimators for convection-diffusion equations Numer. Math. 80 1998 641-663
    • (1998) Numer. Math. , vol.80 , pp. 641-663
    • Verfürth, R.1
  • 44
    • 0001491557 scopus 로고
    • Error estimation and adaptivity in Navier-Stokes incompressible flows
    • J. Wu J.Z. Zhu J. Smelter O.C. Zienkiewicz Error estimation and adaptivity in Navier-Stokes incompressible flows Comput. Mech. 6 1990 259-271
    • (1990) Comput. Mech. , vol.6 , pp. 259-271
    • Wu, J.1    Zhu, J.Z.2    Smelter, J.3    Zienkiewicz, O.C.4
  • 45
  • 47
    • 0026866050 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
    • O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery 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
  • 48
    • 0026869285 scopus 로고
    • The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
    • O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.