This paper constructs a lower order mixed finite element for the linear elasticity problem in 3D. The discrete stresses are piecewise cubic polynomials, and the discrete displacements are discontinuous piecewise quadratic polynomials. The continuity of the discrete stress space is characterized by moving all the edge degrees of freedom of the analogous Hu-Zhang stress element for $P_3$ [Hu, Zhang, Sci. Math. China, 2015, Hu, J. Comput. Math., 2015] to the faces. The macro-element technique is used to define an interpolation operator for proving the discrete stability.

翻译：本文为 3D 线性弹性问题构建了一个较低顺序的混合限量元素。 离散压力是片断的立方体, 离散的偏移是不连续的片断四面体。 离散压力空间的连续性特征是将类似的Hu- Zhang 压力元素的所有边缘自由度移动到面部, 以$P$3 [Hu, Zhang, Sci. Math. China, 2015, Hu, J. Comput. Math., 2015] 。 宏观元素技术用来定义用于证明离散稳定性的内推操作器 。</s>