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Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

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Abstract

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a “smooth + singular” decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.

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Authors and Affiliations

  1. Institute of Mechanics & Advanced Materials, School of Engineering, Cardiff University, Queen’s Building, The Parade, Cardiff, CF24 3AA, Wales, UK

    Octavio A. González-Estrada & Stéphane P. A. Bordas

  2. School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, Australia

    Sundararajan Natarajan

  3. Centro de Investigación de Tecnología de Vehículos (CITV), Universitat Politècnica de València, 46022, Valencia, Spain

    Juan José Ródenas

  4. Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

    Hung Nguyen-Xuan

Authors
  1. Octavio A. González-Estrada
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  2. Sundararajan Natarajan
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  3. Juan José Ródenas
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  4. Hung Nguyen-Xuan
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  5. Stéphane P. A. Bordas
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Correspondence to Stéphane P. A. Bordas.

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González-Estrada, O.A., Natarajan, S., Ródenas, J.J. et al. Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Comput Mech 52, 37–52 (2013). https://doi.org/10.1007/s00466-012-0795-6

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  • DOI: https://doi.org/10.1007/s00466-012-0795-6

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