We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes. This complex includes vector fields and symmetric and traceless tensor fields, interlinked through the conformal Killing operator, the linearized Cotton-York operator, and the divergence operator, respectively. This leads to discrete versions of transverse traceless (TT) tensors and York splits in general relativity. We provide bubble complexes and investigate supersmoothness to facilitate the construction. We show the exactness of the finite element complex on contractible domains.

翻译：我们构建了四面体网格上共形复形的有限元子复形族。该复形包含向量场、对称无迹张量场，它们分别通过共形Killing算子、线性化Cotton-York算子与散度算子相互关联。由此得到广义相对论中横波无迹（TT）张量与York分解的离散版本。我们引入泡复形并研究超光滑性以辅助构造，并证明了该有限元复形在可收缩区域上的正合性。