Lower order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem

Hong Ying Man; Jun Hu; Zhong Ci Shi

doi:10.1142/S0218202509003358

Lower order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem

Hong Ying Man^*
, Jun Hu
, Zhong Ci Shi

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

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	https://doi.org/10.1142/S0218202509003358
Publication status	Published - Jan 2009

Keywords

Elasticity
Mixed method
Nonconforming?nite element

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10.1142/S0218202509003358

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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 \$\textbackslash{}mathcal\{O\}(h)\$ for both the displacement and stress.",

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AU - Hu, Jun

AU - Shi, Zhong Ci

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N2 - 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.

AB - 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.

KW - Elasticity

KW - Mixed method

KW - Nonconforming?nite element

UR - https://www.scopus.com/pages/publications/65249137619

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DO - 10.1142/S0218202509003358

M3 - Article

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JO - Mathematical Models and Methods in Applied Sciences

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ER -

Lower order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem

Abstract

Keywords

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