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 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剖分上构建了相容的有限元弹性复形。弹性复形中，位移、应变、应力和载荷空间通过表示变形、不协调性和散度的微分算子连接。针对这些分量空间中的每一个，我们展示了Worsey-Farin网格上对应的有限元空间。为这些有限元发展了单解自由度，这也在光滑函数上导出了交换（上链）投影。这些复形中空间的一个显著特征是网格子单纯形上缺乏外在的超光滑性。值得注意的是，该复形首次在三维空间中导出了无顶点或边自由度的（强）对称应力元。此外，最低阶应力空间仅使用分段线性函数，这是应力空间可行多项式阶数的最低值。