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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{O}(h^2)$\end{document} is obtained for the displacement, along with a suboptimal, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{O}(h)$\end{document}, error estimate for the stress, in both dimensions.