A new nonconforming mixed finite element method for linear elasticity

We have developed new nonconforming mixed finite element methods for linear elasticity with a pure traction (displacement) boundary condition based on the Hellinger-Reissner variational principle using rectangular elements. Convergence analysis yields an optimal (suboptimal) convergence rate of O(h(2)) (O(h3/2)) for the L-2-error of the stress and O(h) for the displacement in the pure traction (displacement) boundary problem. However, numerical experiments have yielded optimal-order convergence rates for both stress and displacement in both problems and have shown superconvergence for the displacement at the midpoint of each element. Moreover, we observed that the optimal convergence rates are still valid for large lambda.