Abstract
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 $\mathcal{O}(h)$ for both the displacement and stress.
| Original language | English |
|---|---|
| Pages (from-to) | 51-65 |
| Number of pages | 15 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 19 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2009 |
Keywords
- Elasticity
- Mixed method
- Nonconforming?nite element
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Man, H. Y., Hu, J., & Shi, Z. C. (2009). Lower order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem. Mathematical Models and Methods in Applied Sciences, 19(1), 51-65. https://doi.org/10.1142/S0218202509003358