Regge metrics with enhanced trace
This work addresses a technical problem in finite element methods for researchers in computational physics and geometry, but appears incremental as it builds on existing Regge metrics.
The authors introduced variants of Regge finite element metrics with enhanced trace properties, ensuring the trace operator is surjective to a continuous function space, and sketched applications in general relativity, incompressible elasticity, and conformal geometry.
We introduce variants of Regge finite element metrics with enhanced properties of the trace. In particular the trace operator is surjective to a finite element space of continuous functions. Multiplying these scalar functions by the identity tensor brings one back to the finite element space of metrics. The metrics can be based on high order polynomials and be constructed on refinements, such as the Clough-Tocher or Worsey-Farin splits. Potential applications to general relativity, incompressible elasticity and conformal geometry are sketched.