New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined 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. Basis functions are explicitly given in terms of barycentric coordinates. Low-order conforming finite element elasticity complexes starting from the Bell element, are developed in two dimensions. These finite elements for symmetric tensors are applied to devise robust mixed finite element methods for the linear elasticity problem, which possess the uniform error estimates with respect to the Lam\'{e} coefficient $\lambda$, and superconvergence for the displacement. Numerical results are provided to verify the theoretical convergence rates.

翻译：在任意维度上构造了新的低阶 $H(\textrm{div})$ 相容对称张量有限元。形函数空间通过用 $(d+1)$ 阶法向-法向面气泡空间丰富对称二次多项式空间来定义。其简化版本仅有 $d(d+1)^2$ 个自由度。基函数以重心坐标显式给出。在二维情形下，发展了从Bell元开始的低阶相容有限元弹性复形。这些对称张量有限元被应用于设计针对线性弹性问题的鲁棒混合有限元方法，该方法具有关于 Lamé 系数 $\lambda$ 的一致误差估计以及位移的超收敛性。提供了数值结果以验证理论收敛速率。