We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators representing deformation, incompatibility, and divergence. For each of these component spaces, a corresponding finite element space on Worsey-Farin meshes is exhibited. Unisolvent degrees of freedom are developed for these finite elements, which also yields commuting (cochain) projections on smooth functions. A distinctive feature of the spaces in these complexes is the lack of extrinsic supersmoothness at subsimplices of the mesh. Notably, the complex yields the first (strongly) symmetric stress finite element with no vertex or edge degrees of freedom in three dimensions. Moreover, the lowest order stress space uses only piecewise linear functions which is the lowest feasible polynomial degree for the stress space.

翻译：我们在三维Worsey-Farin分割上构造了协调的有限元弹性复形。位移、应变、应力和载荷空间通过代表变形、非协调性和散度的微分算子连接在弹性复形中。针对每个分量空间，我们展示了Worsey-Farin网格上相应的有限元空间。为这些有限元建立了唯一可解的自由度，这同时给出了光滑函数上的交换（上同调）投影。这些复形空间的一个显著特征是在网格的子单纯形上缺乏外在超光滑性。值得注意的是，该复形首次给出了三维空间中不含顶点或边自由度的（强）对称应力有限元。此外，最低阶应力空间仅使用分片线性函数，这是应力空间可行多项式次数中的最低阶。