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On the Convergence of Adaptive Finite Element Methods

  1. Carsten Carstensen*

Article first published online: 5 NOV 2004

DOI: 10.1002/pamm.200410007

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PAMM

PAMM

Volume 4, Issue 1, pages 27–30, December 2004

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How to Cite

Carstensen, C. (2004), On the Convergence of Adaptive Finite Element Methods. Proc. Appl. Math. Mech., 4: 27–30. doi: 10.1002/pamm.200410007

Author Information

  1. Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

*Phone: +00 49 30 2093 5489, Fax: +00 49 30 2093 5859

Publication History

  1. Issue published online: 5 NOV 2004
  2. Article first published online: 5 NOV 2004

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References

  • [1]
    M. Ainsworth, J. T. Oden, A posteriori error estimation in finite element analysis, Wiley-Interscience [John Wiley & Sons], New York (2000).
  • [2]
    J. Alberty, C. Carstensen, D. Zarrabi, Adaptive numerical analysis in primal elastoplasticity with hardening, Comp. Math. Appl. Mech. Engrg., 171, (1999), 175–204.
  • [3]
    I. Babuška, T. Strouboulis, The Finite Element Method and its Reliability, The Clarendon Press Oxford University Press, (2001), xii+802.
  • [4]
    P. Binev, W. Dahmen, R. DeVore, Adaptive Finite Element methods with Convergence Rates, Num. Math., Published online: January 8, 2004, DOI: 10.1007/s00211-003-0492-7.
  • [5]
    C. Carstensen, Domain decomposition for a non-smooth convex minimisation problem and its application to Plasticity, NLAA, 4, 3, (1997), 1–13.
  • [6]
    C. Carstensen, Numerical analysis of primal elastoplasticity with hardening, Numer. Math., 82, (1999), 577–597.
  • [7]
    C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element method, M2AN, 33, (1999), 1187–1202.
  • [8]
    C. Carstensen, An adaptive mesh-refining algorithm allowing for an H1-stable L2-projection onto Courant finite element spaces, Constr. Approx., (2003), Published online: October 10, 2003, DOI: 10.1007/s00365-003-0550-5.
  • [9]
    C. Carstensen, Convergence of adaptive finite element methods for convex minimisation problems, In preparation (2004).
  • [10]
    C. Carstensen, Convergence of Adaptive Finite Element Methods in Computational Mechanics. In preparation (2004).
  • [11]
    C. Carstensen, J. Alberty, Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening, Comp. Meth. Appl. Mech. Engrg., 192, (2003), 1435–1450.
  • [12]
    C. Carstensen, J. Bolte, Adaptive Mesh-Refining Algorithm for Courant Finite Elements in Matlab. Part I, (2004).
  • [13]
    C. Carstensen, R. Verfürth, Edge residuals dominate a posteriori error estimates for low orderfinite element methods, SIAM J. Numer. Anal., 36, 5, (1999), 1571–1587.
  • [14]
    W. Dörfler A convergent adaptive algorithm for Poisson 's equation, SIAM J. Numer. Anal., 33, 3, (1996), 1106–1124.
  • [15]
    K. Eriksson, E. Estep, P. Hansbo, C. Johnson, Computational Diferential Equations, Cambridge University Press, Cambridge, (1995).
  • [16]
    W. Han, B. D. Reddy, Plasticity, Mathematical Theory and Numerical Analysis. Springer, New York (1999).
  • [17]
    C. Johnson, P. Hansbo, Adaptive finite element methods in computational mechanics, Comp. Meth. Appl. Mech. Engrg., 101, (1992), 143–181.
  • [18]
    P. Morin, R. H. Nochetto, K. G. Siebert, Convergence of adaptive finite element methods, SIAM Review, 44, (2003), 631–658.
  • [19]
    J. Necas, I. Hlavacek, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, New York (1981).
  • [20]
    R. Rannacher, F. T. Suttmeier, A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity, Comput. Mech., 21, 2, (1998), 123–133.
  • [21]
    R. Rannacher, F. T. Suttmeier, A posteriori error estimation and mesh adaptation for finite element models in elasto -plasticity, Comput. Methods Appl. Mech. Eng., 176, 1-4, (1999), 333–361.
  • [22]
    J. C. Simo, T. J. R. Hughes, ComputationalInelasticity, Springer-Verlag, New York (1998).
  • [23]
    R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, New York, Leipzig (1996).
  • [24]
    A. Veeser, Convergent adaptive finite elements for the nonlinear Laplacian. Numer. Math., 92, 4, (2002), 743–770.
  • [25]
    E. Zeidler, Nonlinear functional analysis and its applications I and IV. Springer-Verlag, New York (1985) and (1988).
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