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J. Comp. Math., 23 (2005), pp. 441-448. |
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A Mixed Finite Element Method For The Contact Problem In Elasticity Dong-ying Hua 1, Lie-heng Wang 2 1 ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China; and Graduate School of the Chinese Academy of Science, Beijing 100080, China2 LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Abstract Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from $\mathcal{O}(h^{3/4})$ to quasi-optimal $\mathcal{O}(h|logh|^{1/4})$. If stronger but reasonable regularity is available, the convergence rate can be optimal $\mathcal{O}(h)$.
Key words: Contact problem; Mixed finite element method. |