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A family of mixed finite elements is proposed for solving the first ordersystem of linear elasticity equations in any space dimension, where the stressfield is approximated by symmetric finite element tensors.  This family of elements has a perfect matching between the stress componentsand the displacement.  The discrete spaces for the normal stress $\sigma_{ii}$, the shear stress$\sigma_{ij}$ and the displacement $u_i$ are  $\operatorname{span}\{1,x_i\}$, $\operatorname{span}\{1,x_i,x_j\}$ and$\operatorname{span}\{1\}$, respectively, on rectangular grids.  In particular, the definition remains the same for all space dimensions. As aresult of these choices, the theoretical analysis is independent of the spatialdimension as well. In 1D, this element is nothing else but the 1DRaviart-Thomas element, which is the only conforming element in this family. In2D and higher dimensions, they are new elements but of the minimal degrees offreedom. The total degrees of freedom per element is 2 plus 1 in 1D, 7 plus 2in 2D, and 15 plus 3 in 3D.  The previous record of the least degrees of freedom is, 13 plus 4 in 2D, and54 plus 12 in 3D, on the rectangular grid.  These elements are the simplest element for any space dimension.  The well-posedness condition and the optimal a priori error estimate of thefamily of finite elements are proved for both pure displacement and tractionproblems. Numerical tests in 2D and 3D are presented to show a superiority ofthe new element over others, as a superconvergence is surprisingly exhibited.

The simplest mixed finite element method for linear elasticity in the symmetric formulation on $n$-rectangular grids