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 ( h 2 ) ) O(h)\;(O({h^2})) error estimates in the energy ( L 2 ) ({L^2}) 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.