TY - JOUR
T1 - Quadrilateral Finite Elements for Planar Linear Elasticity Problem with Large Lamé Constant
AU - Cheng , Xiaoliang
AU - Huang , Hongci
AU - Zou , Jun
JO - Journal of Computational Mathematics
VL - 4
SP - 357
EP - 366
PY - 1998
DA - 1998/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9166.html
KW - Planar linear elasticity, optimal error estimates, large Lamé constant, locking phenomenon.
AB - <p style="text-align: justify;">In this paper, we discuss the quadrilateral finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the $L^2$-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lamé&nbsp;constant $\lambda$. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Numerical experiments are given which are consistent with our theory.&nbsp;</p>