Regge calculus can be interpreted in a finite element context and provides natural spaces of metrics for discrete Riemannian geometry. For some applications, such as conformal geometry and general relativity, it seems worthwhile to construct variants with enhanced properties of the trace. We define spaces where the trace operator is surjective to a finite element space of continuous scalars and such that multiplying these scalars by the identity tensor maps back into the finite element space of metrics. This creates spaces that are invariant under the Hooke operator defined in elasticity by the Lamé parameters and the operator S linking rows in the BGG diagram and appearing in some formulations of GR. In particular these operators are stably invertible in the discrete setting whenever they are invertible in the continuous setting, contrary to the case of original Regge metrics.
Joint work with Ting Lin, Peking University
Reference: arXiv:2603.13977