We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de~Rham complexes, and smoother finite element differential forms.

中文翻译：

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三维 Alfeld 分裂上的离散弹性复形

我们在四面体的 Alfeld 分裂上构造了一致的有限元弹性复合体。该复合体由矢量场和对称张量场组成，分别通过线性变形算子、线性曲率算子和发散算子相互连接。该构造基于代数机制，该机制从 de~Rham 复数和更平滑的有限元微分形式导出弹性复数。