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 - <p style="text-align: justify;">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.</p>