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Uniform convergence and a posteriori error estimators for the enhanced strain finite element method

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Summary.

Enhanced strain elements, frequently employed in practice, are known to improve the approximation of standard (non-enhanced) displacement-based elements in finite element computations. The first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes: it is shown that such schemes are locking-free in the incompressible limit, in the sense that the error bound in the a priori estimate is independent of the relevant Lamé constant. The second contribution is a residual-based a posteriori error estimate; the L 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals.

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Authors and Affiliations

  1. Faculty of Mathematics, Ruhr-University, 44780, Bochum, Germany

    D. Braess

  2. Institute for Applied Mathematics and Numerical Analysis, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    C. Carstensen

  3. Department of Mathematics and Applied Mathematics, University of Cape Town, 7701, Rondebosch, South Africa

    B.D. Reddy

Authors
  1. D. Braess
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  2. C. Carstensen
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  3. B.D. Reddy
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Correspondence to D. Braess.

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Mathematics Subject Classification (2000): 65N30

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Braess, D., Carstensen, C. & Reddy, B. Uniform convergence and a posteriori error estimators for the enhanced strain finite element method. Numer. Math. 96, 461–479 (2004). https://doi.org/10.1007/s00211-003-0486-5

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  • DOI: https://doi.org/10.1007/s00211-003-0486-5

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