Locking-free nonconforming finite elements for three-dimensional elasticity problem

Two locking-free nonconforming finite elements are presented for three-dimensional elasticity problem with pure displacement boundary condition. Convergence rate of the elements are uniformly optimal with respect to λ. The energy norm and L2 norm errors are O(h2) and O(h3), respectively. Lastly, a numerical experiment is carried out, which coincides with the theoretical analysis.