LINEAR FINITE-ELEMENT METHODS FOR PLANAR LINEAR ELASTICITY

A linear nonconforming (conforming) displacement finite element method for the pure displacement (pure traction) problem in two-dimensional linear elasticity for a homogeneous isotropic elastic material is considered. In the case of a convex polygonal configuration domain, O(h) (O(h2)) error estimates in the energy (L2) norm are obtained. The convergence rate does not deteriorate for nearly incompressible material. Furthermore, the convergence analysis does not rely on the theory of saddle point problems.