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Zbl 1142.65369
Hua, Dongying; Wang, Lieheng
The nonconforming finite element method for Signorini problem. (English)
[J] J. Comput. Math. 25, No. 1, 67-80 (2007). ISSN 0254-9409; ISSN 1991-7139/e

Summary: The authors present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. The authors show if the displacement field is of $H^2$ regularity, then the convergence rate can be improved from $O(h^{3/4})$ to quasi-optimal $O(h|\log h|^{1/4})$ 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 $O(h)$ as expected by the linear approximation.

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

Keywords: nonconforming finite element method; Signorini problem; convergence; variational inequality

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