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

González-Estrada, Octavio A., Natarajan, Sundararajan, Ródenas, Juan José, Nguyen-Xuan, Hung and Bordas, Stephane Pierre Alain ORCID: 2013. Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics 52 (1) , pp. 37-52. 10.1007/s00466-012-0795-6

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TJ Mechanical engineering and machinery
Uncontrolled Keywords: Smoothed finite element method; Error estimation; Statical admissibility; SPR-CX; Singularity; Recovery
Publisher: Springer
ISSN: 0178-7675
Funders: Royal Academy of Engineering, Leverhulme Trust, EPSRC, European Research Council (ERC), EU FP7, Ministerio de Ciencia e Innovación (Spain), Universitat Politècnica de València, Generalitat Valenciana
Last Modified: 21 Oct 2022 10:23

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