Reference : Efficient recovery-based error estimation for the smoothed finite element method for ...
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Computational Sciences
Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity
González-Estrada, O. A. [Institute of Mechanics and Advanced Materials, School of Engineering, Cardiff University Queen's Building, The Parade, Cardiff CF24 3AA, United Kingdom]
Natarajan, S. [School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW, Australia]
Ródenas, J. J. [Centro de Investigación de Tecnología de Vehículos (CITV), Universitat Politècnica de València, 46022 Valencia, Spain]
Nguyen-Xuan, H. [Department of Mechanics, Faculty of Mathematics and Computer Science, Vietnam National University, Ho Chi Minh City, Viet Nam]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Computational Mechanics
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[en] Error estimation ; Recovery ; Singularity ; Smoothed finite element method ; SPR-CX ; Statical admissibility ; Error control techniques ; Finite element approximations ; Finite element techniques ; Linear elastic structural mechanics ; Elasticity ; Enhanced recovery ; Error analysis ; Estimation ; Finite element method ; Quality control
[en] 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. © 2012 Springer-Verlag.
Royal Academy of Engineering; Leverhulme Trust
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