A finite element elasticity complex on tetrahedral meshes is devised. The $H^1$ conforming finite element is the smooth finite element developed by Neilan for the velocity field in a discrete Stokes complex. The symmetric div-conforming finite element is the Hu-Zhang element for stress tensors. The construction of an $H(\textrm{inc})$-conforming finite element for symmetric tensors is the main focus of this paper. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of the trace of the $\textrm{inc}$ operator. The polynomial elasticity complex and Koszul elasticity complex are created to derive the decomposition of polynomial tensor spaces. The trace of the $\textrm{inc}$ operator is induced from a Green's identity. Trace complexes and bubble complexes are also derived to facilitate the construction. Our construction appears to be the first $H(\textrm{inc})$-conforming finite elements on tetrahedral meshes without further splits.

翻译：设计了四面环形外壳的有限元素弹性综合体。 $H $1 符合的有限元素是Nelan在离散的斯托克斯复合体中为速度场开发的平滑的有限元素。 对称的 div- 相容性元素是用于应力加压器的Hu- Zhang 元素。 建造一个 $H (\ textrm{inc}) 的对称的对称质元素是本文的主要焦点。 构造中的关键工具是多元感应空间的分解和对 $\ textrm{ inc} 操作器的追踪的定性。 多元感弹性复合和 Koszul 弹性复合元素的创建是为了得出多元性抗震力空间的分解。 $( textrm{ inc} 操作器的痕迹来自绿色的特性。 跟踪复合体和泡泡复合体也用来促进构造。 我们的构造似乎是第一个没有进一步裂变制的基质成的 $H( textrmrm) 。