A unified construction of $H(\textrm{div})$-conforming finite elements, including vector element, symmetric matrix element, and traceless matrix element, is developed in this work. It is based on the geometric decomposition of Lagrange elements into bubble functions on each sub-simplex. Then the vector or matrix at each sub-simplex is decomposed into the tangential and the normal components. The tangential component forms the polynomial bubble function space and the normal component characterizes the trace of div operator. Some degrees of freedom on the normal component can be redistributed facewisely. Discrete inf-sup conditions are verified.

翻译：在此工程中开发了 $H (\ textrm{div}) 的统一构造, 包括矢量元素、 对称矩阵元素和无微量矩阵元素在内的符合 $H (\ textrm{div}) 的有限元素。 它基于 Lagrange 元素的几何分解为每个子质的泡泡函数。 然后将每个子质的矢量或矩阵分解为相近和正常的成分。 相近成分构成多元泡泡功能空间和正常成分的特性。 正常组件的某些自由度可以以对面方式进行再分配 。 将核实混入条件 。