Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

Ainsworth, Mark and Rankin, Richard Andrew Robert (2011) Realistic computable error bounds for three dimensional finite element analyses in linear elasticity. Computer Methods in Applied Mechanics and Engineering, 200 (21-22). pp. 1909-1926. ISSN 0045-7825 (https://doi.org/10.1016/j.cma.2011.01.017)

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Abstract

We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.

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