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

Geometric Decompositions of $H(\textrm{div})$-conforming Finite Element Tensors, Part I: Vector and Matrix Functions