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Volumn 130, Issue 1-2, 1996, Pages 93-113

A subdomain residual method for a posteriori error estimates of finite element solutions of viscoelastic fluid flows

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FLUID FLOW; VISCOELASTIC FLUIDS;

EID: 0030088260     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7825(95)00910-8     Document Type: Article
Times cited : (7)

References (29)
  • 1
    • 84985315731 scopus 로고
    • A posteriori error estimates for the finite element method
    • I. Babuska and 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
    • Babuska, I.1    Rheinboldt, W.C.2
  • 2
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. Babuska and W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 (1978) 736-754.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuska, I.1    Rheinboldt, W.C.2
  • 3
    • 0021510869 scopus 로고
    • Adaptive finite element methods for flow problems with moving boundaries. Part I: Variational principles and a posteriori estimates
    • L. Demkowicz, J.T. Oden and T. Strouboulis, Adaptive finite element methods for flow problems with moving boundaries. Part I: Variational principles and a posteriori estimates, Comput. Methods Appl. Mech. Engrg. 46 (1984) 217-251.
    • (1984) Comput. Methods Appl. Mech. Engrg. , vol.46 , pp. 217-251
    • Demkowicz, L.1    Oden, J.T.2    Strouboulis, T.3
  • 4
    • 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
  • 5
    • 84966215690 scopus 로고
    • Some a posteriori error estimates for elliptic partial differential equations
    • R.E. Bank and A. Weiser, Some a posteriori error estimates for elliptic partial differential equations, Math. Comp. 44 (1985) 283-301.
    • (1985) Math. Comp. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 6
    • 0039760781 scopus 로고
    • Analysis of a local a posteriori error estimate for elliptic equations
    • I. Babuska, O.C. Zienkiewicz, J.J. Gago and E.R. de A. Oliveira, eds., Wiley, Chichester, UK
    • R.E. Bank, Analysis of a local a posteriori error estimate for elliptic equations, in: I. Babuska, O.C. Zienkiewicz, J.J. Gago and E.R. de A. Oliveira, eds., Accuracy Estimates and Adaptive Refinement in Finite Element Computations (Wiley, Chichester, UK, 1986) 119-128.
    • (1986) Accuracy Estimates and Adaptive Refinement in Finite Element Computations , pp. 119-128
    • Bank, R.E.1
  • 7
    • 0002071619 scopus 로고
    • Adaptive methods for problems in solid and fluid mechanics
    • I. Babuska, O.C. Zienkiewicz, J.J. Gago and E.R. de A. Oliveira, eds., Wiley, Chichester, UK
    • J.T. Oden, L. Demkowicz, T. Strouboulis and P. Devloo, Adaptive methods for problems in solid and fluid mechanics, in: I. Babuska, O.C. Zienkiewicz, J.J. Gago and E.R. de A. Oliveira, eds., Accuracy Estimates and Adaptive Refinement in Finite Element Computations (Wiley, Chichester, UK, 1986), 249-280.
    • (1986) Accuracy Estimates and Adaptive Refinement in Finite Element Computations , pp. 249-280
    • Oden, J.T.1    Demkowicz, L.2    Strouboulis, T.3    Devloo, P.4
  • 8
    • 0023289037 scopus 로고
    • Error estimates and automatic time step control for non-linear parabolic problems, I
    • K. Eriksson and C. Johnson, Error estimates and automatic time step control for non-linear parabolic problems, I, SIAM J. Numer. Anal. 24 (1987) 12-23.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 12-23
    • Eriksson, K.1    Johnson, C.2
  • 9
    • 84966258545 scopus 로고
    • Crosswind smear and pointwise errors in streamline diffusion finite element methods
    • C. Johnson, A. Schatz and L. Wahlbin, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp. 49 (1987) 25-38.
    • (1987) Math. Comp. , vol.49 , pp. 25-38
    • Johnson, C.1    Schatz, A.2    Wahlbin, L.3
  • 10
    • 0023288565 scopus 로고
    • A simple error estimator and adaptive procedure for practical engineering analysis
    • O.C. Zienkiewicz and 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
  • 11
    • 0023438281 scopus 로고
    • A posteriori estimates of the solution error caused by discretization in the finite element, finite difference and boundary element methods
    • D.W. Kelly, R.J. Mills, J.A. Reizes and A.D. Miller, A posteriori estimates of the solution error caused by discretization in the finite element, finite difference and boundary element methods, Int. J. Numer. Methods Engrg. 24 (1987) 1921-1939.
    • (1987) Int. J. Numer. Methods Engrg. , vol.24 , pp. 1921-1939
    • Kelly, D.W.1    Mills, R.J.2    Reizes, J.A.3    Miller, A.D.4
  • 12
    • 0001562231 scopus 로고
    • Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations
    • C. Johnson, Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 25 (1988) 908-926.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 908-926
    • Johnson, C.1
  • 13
    • 0024945154 scopus 로고
    • Toward a universal h - p adaptive finite element strategy. Part 2, a posteriori error estimates
    • J.T. Oden, L. Demkowicz, T. Westermann and W. Rachowicz, Toward a universal h - p adaptive finite element strategy. Part 2, A posteriori error estimates, Comput. Methods Appl. Mech. Engrg. 77 (1989) 113-180.
    • (1989) Comput. Methods Appl. Mech. Engrg. , vol.77 , pp. 113-180
    • Oden, J.T.1    Demkowicz, L.2    Westermann, T.3    Rachowicz, W.4
  • 14
    • 0025208435 scopus 로고
    • A posteriori error estimation of finite element approximations in fluid mechanics
    • T. Strouboulis and 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
  • 15
    • 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 and 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) 182-203.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.82 , pp. 182-203
    • Oden, J.T.1    Demkowicz, L.2    Rachowicz, W.3    Westermann, T.A.4
  • 16
    • 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
  • 17
    • 0026876667 scopus 로고
    • Recent experiences with error estimation and adaptivity, Part I: Review of error estimators for scalar elliptic problems
    • T. Strouboulis and K.A. Haque, Recent experiences with error estimation and adaptivity, Part I: Review of error estimators for scalar elliptic problems, Comput. Methods Appl. Mech. Engrg. 97 (1992) 399-436.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.97 , pp. 399-436
    • Strouboulis, T.1    Haque, K.A.2
  • 18
    • 0026973251 scopus 로고
    • A procedure for a posteriori error estimation for h - p finite element methods
    • M. Ainsworth and J.T. Oden, A procedure for a posteriori error estimation for h - p finite element methods, Comput. Methods Appl. Mech. Engrg. 101 (1992) 72-96.
    • (1992) Comput. Methods Appl. Mech. Engrg. , vol.101 , pp. 72-96
    • Ainsworth, M.1    Oden, J.T.2
  • 19
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using element residual methods
    • M. Ainsworth and J.T. Oden, A unified approach to a posteriori 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
  • 20
    • 0027974409 scopus 로고
    • An a posteriori error estimate for finite element approximations of the Navier-Stokes equations
    • J.T. Oden, W. Wu and M. Ainsworth, An a posteriori 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
  • 21
    • 84987515903 scopus 로고
    • On the quality of viscoelastic flow solutions: An adaptive refinement study of a Newtonian and a Maxwell fluid
    • R.R. Rao and B.A. Finlayson, On the quality of viscoelastic flow solutions: An adaptive refinement study of a Newtonian and a Maxwell fluid, Int. J. Numer. Methods Fluids 11 (1990) 571-585.
    • (1990) Int. J. Numer. Methods Fluids , vol.11 , pp. 571-585
    • Rao, R.R.1    Finlayson, B.A.2
  • 22
    • 0026054365 scopus 로고
    • Adaptive refinement of a viscoelastic flow problem with the explicitly elliptic momentum equation
    • R.R. Rao and B.A. Finlayson, Adaptive refinement of a viscoelastic flow problem with the explicitly elliptic momentum equation, J. non-Newt. Fluid Mech. 38 (1991) 223-246.
    • (1991) J. Non-Newt. Fluid Mech. , vol.38 , pp. 223-246
    • Rao, R.R.1    Finlayson, B.A.2
  • 23
    • 0028401054 scopus 로고
    • An a posteriori error estimate and adaptive refinement procedure for viscoelastic fluid flows: The modified upper-convected Maxwell model
    • H. Jin and R.I. Tanner, An a posteriori error estimate and adaptive refinement procedure for viscoelastic fluid flows: The modified upper-convected Maxwell model, Comput. Mech. 13 (1994) 400-413.
    • (1994) Comput. Mech. , vol.13 , pp. 400-413
    • Jin, H.1    Tanner, R.I.2
  • 24
    • 0019607241 scopus 로고
    • Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.1    Hughes, T.J.R.2
  • 25
    • 0023999282 scopus 로고
    • Impact of the constitutive equation and singularity on the calculation of stick-slip flow: The modified upper-convected Maxwell model (MUCM)
    • M.R. Apelian, R.C. Armstrong and R.A. Brown, Impact of the constitutive equation and singularity on the calculation of stick-slip flow: The modified upper-convected Maxwell model (MUCM), J. non-Newt. Fluid Mech. 27 (1988) 299-321.
    • (1988) J. Non-Newt. Fluid Mech. , vol.27 , pp. 299-321
    • Apelian, M.R.1    Armstrong, R.C.2    Brown, R.A.3
  • 26
    • 0022681271 scopus 로고
    • A new finite element method for computational fluid dynamics: II. Beyond SUPG
    • T.J.R. Hughes, M. Mallet and A. Mizukami, A new finite element method for computational fluid dynamics: II. Beyond SUPG, Comput. Methods Appl. Mech. Engrg. 54 (1986) 341-355.
    • (1986) Comput. Methods Appl. Mech. Engrg. , vol.54 , pp. 341-355
    • Hughes, T.J.R.1    Mallet, M.2    Mizukami, A.3


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