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Volumn 87, Issue 11-12, 2007, Pages 860-876

A functional type a posteriori error analysis for the Ramberg-Osgood model

Author keywords

A posteriori error estimates; Norton Hoff model; Ramberg Osgood equations; Variational methods

Indexed keywords


EID: 37649004075     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200710350     Document Type: Article
Times cited : (2)

References (40)
  • 1
    • 0003796630 scopus 로고
    • Academic Press, New York, San Francisco, London
    • R. A. Adams, Sobolev spaces (Academic Press, New York, San Francisco, London, 1975).
    • (1975) Sobolev spaces
    • Adams, R.A.1
  • 3
    • 0027306344 scopus 로고
    • Local a posteriori error estimators for variational inequalities
    • M. Ainsworth, J. T. Oden, and C. Y. Lee, Local a posteriori error estimators for variational inequalities, Num. Meth. for PDE 9, 23-33 (1993).
    • (1993) Num. Meth. for PDE , vol.9 , pp. 23-33
    • Ainsworth, M.1    Oden, J.T.2    Lee, C.Y.3
  • 5
    • 0030383153 scopus 로고    scopus 로고
    • A feed-back approach to error control in finite element methods: Basic approach and examples, East-West
    • R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: basic approach and examples, East-West J. Num. Math. 4 237-264 (1996).
    • (1996) J. Num. Math , vol.4 , pp. 237-264
    • Becker, R.1    Rannacher, R.2
  • 6
    • 37649010717 scopus 로고    scopus 로고
    • 1 regularity. In: Boundary Value Problems for Partial Differential Equations and Applications, edited by J.L. Lions and C. Baiocchi, no. 29 in Research Notes in Applied Mathematics. Masson, Paris, 1993, pp. 3-26.
    • 1 regularity. In: Boundary Value Problems for Partial Differential Equations and Applications, edited by J.L. Lions and C. Baiocchi, no. 29 in Research Notes in Applied Mathematics. Masson, Paris, 1993, pp. 3-26.
  • 7
    • 33847066350 scopus 로고    scopus 로고
    • Smoothness of weak solutions of the Ramberg/Osgood equations on plane domains
    • M. Bildhauer and M. Fuchs, Smoothness of weak solutions of the Ramberg/Osgood equations on plane domains, Z. Angew. Math. Mech. 87, 70-76 (2007).
    • (2007) Z. Angew. Math. Mech , vol.87 , pp. 70-76
    • Bildhauer, M.1    Fuchs, M.2
  • 8
    • 77952288381 scopus 로고    scopus 로고
    • M. Bildhauer and M. Fuchs, Continuity properties of the stress tensor in the 3-dimensional Ramberg/Osgood model. J. Appl. Anal. 13, in press (2007).
    • M. Bildhauer and M. Fuchs, Continuity properties of the stress tensor in the 3-dimensional Ramberg/Osgood model. J. Appl. Anal. 13, in press (2007).
  • 9
    • 37649002421 scopus 로고    scopus 로고
    • M. Bildhauer and S. Repin, Estimates for the deviation from exact solutions of variational problems with power growth functionals, Zap. Nauch. Semi. (POMI) 336, 5-24 (2006).
    • M. Bildhauer and S. Repin, Estimates for the deviation from exact solutions of variational problems with power growth functionals, Zap. Nauch. Semi. (POMI) 336, 5-24 (2006).
  • 10
    • 33847107539 scopus 로고    scopus 로고
    • A posteriori error estimates for stationary slow flows of power-law fluids
    • M. Bildhauer, M. Fuchs, and S. Repin, A posteriori error estimates for stationary slow flows of power-law fluids, J. Non-Newtonian Fluid Mech. 142, 112-122 (2007).
    • (2007) J. Non-Newtonian Fluid Mech , vol.142 , pp. 112-122
    • Bildhauer, M.1    Fuchs, M.2    Repin, S.3
  • 11
    • 29144485659 scopus 로고    scopus 로고
    • A posteriori error estimators for obstacle problems - another look
    • D. Braess, A posteriori error estimators for obstacle problems - another look, Num. Math. 101, 415-421 (2005).
    • (2005) Num. Math , vol.101 , pp. 415-421
    • Braess, D.1
  • 12
    • 33845521466 scopus 로고    scopus 로고
    • A posteriori error estimates for finite element approximations of parabolic p-Laplacian
    • C. Carstensen, W. Liu, and N. Yan, A posteriori error estimates for finite element approximations of parabolic p-Laplacian, SIAM J. Numer. Anal. 43, 2294-2319 (2006).
    • (2006) SIAM J. Numer. Anal , vol.43 , pp. 2294-2319
    • Carstensen, C.1    Liu, W.2    Yan, N.3
  • 13
    • 84855485012 scopus 로고
    • Uniformly convex spaces
    • J. A. Clarkson, Uniformly convex spaces, Trans. Am. Math. Soc. 40, 396-414 (1936).
    • (1936) Trans. Am. Math. Soc , vol.40 , pp. 396-414
    • Clarkson, J.A.1
  • 14
    • 0034383447 scopus 로고    scopus 로고
    • Residual type a posteriori error estimates for elliptic obstacle problems
    • Z. Chen and R. H. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems, Num. Math 84, 527-548 (2000).
    • (2000) Num. Math , vol.84 , pp. 527-548
    • Chen, Z.1    Nochetto, R.H.2
  • 15
    • 33751373468 scopus 로고    scopus 로고
    • M. Fuchs and S. Repin, Estimates for the deviation from the exact solutions of variational problems modeling certain classes of generalized Newtonian fluids, Math. Meth. Appl. Sci. (M2AS) 29, 2225-2244 (2006).
    • M. Fuchs and S. Repin, Estimates for the deviation from the exact solutions of variational problems modeling certain classes of generalized Newtonian fluids, Math. Meth. Appl. Sci. (M2AS) 29, 2225-2244 (2006).
  • 16
    • 0038629546 scopus 로고
    • Variational methods for problems from plasticity theory and for generalized Newtonian fluids
    • Springer, Berlin, Heidelberg
    • M. Fuchs and G. Seregin, Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Lecture Notes in Mathematics 1749 (Springer, Berlin, Heidelberg, 2000).
    • (1749) Lecture Notes in Mathematics
    • Fuchs, M.1    Seregin, G.2
  • 17
    • 0022566445 scopus 로고
    • Functional spaces for Norton-Hoff Materials
    • G. Geymonat and P. Suquet, Functional spaces for Norton-Hoff Materials, Math. Meth. Appl. Sci. 8, 206-222 (1986).
    • (1986) Math. Meth. Appl. Sci , vol.8 , pp. 206-222
    • Geymonat, G.1    Suquet, P.2
  • 18
    • 0028420070 scopus 로고
    • Adaptive multilevel methods for obstacle problems
    • R.H.W. Hoppe and R. Kornhuber, Adaptive multilevel methods for obstacle problems, SIAM J. Num. Anal. 31, 301-323 (1994).
    • (1994) SIAM J. Num. Anal , vol.31 , pp. 301-323
    • Hoppe, R.H.W.1    Kornhuber, R.2
  • 21
    • 21244432112 scopus 로고
    • On well-posedness of boundary value problems in the mechanics of continuous media
    • P. P. Mosolov and V. P. Mjasnikov, On well-posedness of boundary value problems in the mechanics of continuous media, Mat. Sbornik 88 (130), 256-284 (1972).
    • (1972) Mat. Sbornik , vol.88 , Issue.130 , pp. 256-284
    • Mosolov, P.P.1    Mjasnikov, V.P.2
  • 22
    • 84956104514 scopus 로고
    • English translation in
    • English translation in Math. USSR Sbornik 17, 257-268 (1972).
    • (1972) Math. USSR Sbornik , vol.17 , pp. 257-268
  • 25
    • 3242779817 scopus 로고
    • Consistance, stabilité, erreurs a priori et a posteriori pour des problèmes non linéaries
    • J. Pousin and J. Rappaz, Consistance, stabilité, erreurs a priori et a posteriori pour des problèmes non linéaries, C. R. Acad. Sci. Paris 312, 699-703 (1991).
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 699-703
    • Pousin, J.1    Rappaz, J.2
  • 26
    • 0000986495 scopus 로고
    • Approximation in elasticity based on the concept of function space
    • W. Prager and J. L. Synge, Approximation in elasticity based on the concept of function space, Quart. Appl. Math. 5, 241-269 (1947).
    • (1947) Quart. Appl. Math , vol.5 , pp. 241-269
    • Prager, W.1    Synge, J.L.2
  • 27
    • 0012656543 scopus 로고    scopus 로고
    • The dual-weighted-residual method for error control and mesh adaption in finite element methods. The mathematics of finite elements and applications X, MAFELAP 1999
    • edited by J. Whiteman Elsevier, Amsterdam
    • R. Rannacher, The dual-weighted-residual method for error control and mesh adaption in finite element methods. The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunei Univ., Uxbridge. Middlesex. GB, June 22-25, 1999, edited by J. Whiteman (Elsevier, Amsterdam, 2000), pp. 97-116.
    • (1999) Proceedings of the 10th conference, Brunei Univ., Uxbridge. Middlesex. GB, June 22-25 , pp. 97-116
    • Rannacher, R.1
  • 28
    • 37649000834 scopus 로고    scopus 로고
    • S. Repin, A posteriori error estimation for nonlinear variational problems by duality theory, Zap. Nauch. Sem. (POMI) 243, 201-214 (1997).
    • S. Repin, A posteriori error estimation for nonlinear variational problems by duality theory, Zap. Nauch. Sem. (POMI) 243, 201-214 (1997).
  • 29
    • 0034403953 scopus 로고    scopus 로고
    • A posteriori error estimation for variational problems with uniformly convex functional
    • S. Repin, A posteriori error estimation for variational problems with uniformly convex functional, Math. Comp. 69, 481-500 (2000).
    • (2000) Math. Comp , vol.69 , pp. 481-500
    • Repin, S.1
  • 30
    • 56849095914 scopus 로고    scopus 로고
    • Two-sided estimates of deviation from exact solutions of uniformly elliptic equations
    • Soc. IX
    • S. Repin, Two-sided estimates of deviation from exact solutions of uniformly elliptic equations, Proc. St. Petersburg Math. Soc. IX (2001), pp. 143-171.
    • (2001) Proc. St. Petersburg Math , pp. 143-171
    • Repin, S.1
  • 31
    • 37649021121 scopus 로고    scopus 로고
    • Translation: Amer. Math, Soc. Tansl. Ser. 2, 209 (Amer. Math. Soc., Providence, RI. 2003).
    • Translation: Amer. Math, Soc. Tansl. Ser. 2, 209 (Amer. Math. Soc., Providence, RI. 2003).
  • 32
    • 37649005596 scopus 로고    scopus 로고
    • Estimates of deviations from exact solutions for some boundary-value problems with incompressibility condition
    • S. Repin, Estimates of deviations from exact solutions for some boundary-value problems with incompressibility condition, Algebra i Analiz 16, 124-161 (2004).
    • (2004) Algebra i Analiz , vol.16 , pp. 124-161
    • Repin, S.1
  • 33
    • 37649003290 scopus 로고    scopus 로고
    • Aposteriori estimates of the accuracy of variational methods for problems with nonconvex t'unctionals
    • S. Repin, Aposteriori estimates of the accuracy of variational methods for problems with nonconvex t'unctionals, Algebra i Analiz 11, 151-182 (1999).
    • (1999) Algebra i Analiz , vol.11 , pp. 151-182
    • Repin, S.1
  • 34
    • 0030406640 scopus 로고    scopus 로고
    • A posteriori error estimation for elasto-plastic problems based on duality theory
    • S. Repin and L. S. Xanthis, A posteriori error estimation for elasto-plastic problems based on duality theory. Comp. Meth. Appl. Math. Eng. 138, 317-339 (1996).
    • (1996) Comp. Meth. Appl. Math. Eng , vol.138 , pp. 317-339
    • Repin, S.1    Xanthis, L.S.2
  • 35
    • 37648998802 scopus 로고    scopus 로고
    • A general approach to a posteriori error estimates for strictly monotone and Lipschitz continuous nonlinear operators illustrated in elasto-plasticity
    • Heidelberg, World Sci. Publ, River Edge. New York
    • M. Schulz and W. L. Wendland. A general approach to a posteriori error estimates for strictly monotone and Lipschitz continuous nonlinear operators illustrated in elasto-plasticity, Proc. 2nd European Conf. Num. Math. Advanced Appl 1997 (Heidelberg) (World Sci. Publ., River Edge. New York, 1998), pp. 572-579.
    • (1997) Proc. 2nd European Conf. Num. Math. Advanced Appl , pp. 572-579
    • Schulz, M.1    Wendland, W.L.2
  • 36
    • 84968521915 scopus 로고
    • A posteriori error estimates for nonlinear problems. Finite element discretisations of elliptic equations
    • M. Schulz and W. L. Wendland. A posteriori error estimates for nonlinear problems. Finite element discretisations of elliptic equations, Math. Comp. 62, 445-475 (1994).
    • (1994) Math. Comp , vol.62 , pp. 445-475
    • Schulz, M.1    Wendland, W.L.2
  • 40
    • 84968521915 scopus 로고
    • A posteriori error estimates for nonlinear problems. Finite element discretisations of elliptic equations
    • R. Verfürth, A posteriori error estimates for nonlinear problems. Finite element discretisations of elliptic equations, Math. Comput. 62, 445-475 (1994).
    • (1994) Math. Comput , vol.62 , pp. 445-475
    • Verfürth, R.1


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