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Volume 25, Issue 1
The Nonconforming Finite Element Method for Signorini Problem

Dongying Hua & Lieheng Wang

J. Comp. Math., 25 (2007), pp. 67-80.

Published online: 2007-02

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  • Abstract

We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of $H^2$ regularity, then the convergence rate can be improved from $\mathcal{O}(h^{3/4})$ to quasi-optimal $\mathcal{O}(h|\log h|^{1/4})$ with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal $\mathcal{O}(h)$ as expected by the linear approximation.

  • Keywords

Nonconforming finite element method, Signorini problem, Convergence rate.

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-67, author = {Dongying Hua and Lieheng Wang}, title = {The Nonconforming Finite Element Method for Signorini Problem}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {1}, pages = {67--80}, abstract = {

We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of $H^2$ regularity, then the convergence rate can be improved from $\mathcal{O}(h^{3/4})$ to quasi-optimal $\mathcal{O}(h|\log h|^{1/4})$ with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal $\mathcal{O}(h)$ as expected by the linear approximation.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8673.html} }
TY - JOUR T1 - The Nonconforming Finite Element Method for Signorini Problem AU - Dongying Hua & Lieheng Wang JO - Journal of Computational Mathematics VL - 1 SP - 67 EP - 80 PY - 2007 DA - 2007/02 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8673.html KW - Nonconforming finite element method, Signorini problem, Convergence rate. AB -

We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of $H^2$ regularity, then the convergence rate can be improved from $\mathcal{O}(h^{3/4})$ to quasi-optimal $\mathcal{O}(h|\log h|^{1/4})$ with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available, the convergence rate can be improved to the optimal $\mathcal{O}(h)$ as expected by the linear approximation.

Dongying Hua and Lieheng Wang. (2007). The Nonconforming Finite Element Method for Signorini Problem. Journal of Computational Mathematics. 25 (1). 67-80. doi:
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