Nonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions

摘要

We present nonconforming, rectangular mixed finite element methods based on the Hellinger-Reissner variational principle in both two and three dimensions and show stability and convergence. An optimal error estimate of $mathcal{O}(h^2)$ is obtained for the displacement, along with a suboptimal, $mathcal{O}(h)$ , error estimate for the stress, in both dimensions.