Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8673
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 1 : pp. 67–80
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Nonconforming finite element method Signorini problem Convergence rate.