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New lower order $H(\textrm{div})$-conforming finite elements for symmetrictensors are constructed in arbitrary dimension. The space of shape functions isdefined by enriching the symmetric quadratic polynomial space with the$(d+1)$-order normal-normal face bubble space. The reduced counterpart has only$d(d+1)^2$ degrees of freedom. In two dimensions, basis functions areexplicitly given in terms of barycentric coordinates. Lower order conformingfinite element elasticity complexes starting from the Bell element, aredeveloped in two dimensions. These finite elements for symmetric tensors areapplied to devise robust mixed finite element methods for the linear elasticityproblem, which possess the uniform error estimates with respect to the Lam\'{e}coefficient $\lambda$, and superconvergence for the displacement. Numericalresults are provided to verify the theoretical convergence rates.

New lower order mixed finite element methods for linear elasticity