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 -

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 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.