In this paper, we propose a first-order rectangular nonconforming element for the stress-displacement system derived from the Hellinger–Reissner variational principle for the three-dimensional elasticity problem. We show that the discrete inf–sup condition holds for this scheme. Based on some superconvergence of the consistency error, we prove the optimal error estimate of [Formula: see text] for both the displacement and stress.
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Man et al. (2009) studied this question.
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