New low-order \({H}({{\text {div}}})\)-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 Lamé coefficient \({\lambda }\), and superconvergence for the displacement. Numerical results are provided to verify the theoretical convergence rates.

在任意维度构造对称张量的新低阶\({H}({{\text {div}}})\)一致有限元。形函数空间是通过用\({(d+1)}\)阶正态-正态面气泡空间丰富对称二次多项式空间来定义的。简化的对应部分仅具有\({d(d+1)}^{{2}}\)自由度。基函数以重心坐标明确给出。从贝尔元素开始，低阶一致有限元弹性复合体在二维中得到发展。这些对称张量的有限元被应用于设计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\({\lambda }\) 的均匀误差估计和位移的超收敛性。提供数值结果来验证理论收敛速度。