Regge calculus is an approximation scheme for General Relativity, which has been introduced in early-sixties and has been adopted both in numerical relativity and numerical quantum relativity. In contrast to its widespread use in computational science, there does not seem to exist much theory on whether the Regge calculus is actually consistent - i.e. whether there is some degree of exactness (like mesh width) we can adapt arbitrarly to obtain a solution with arbitrarly small error (say in some Sobolev-norm).
In fact there has been debate about this:
- The Regge Calculus is not an approximation to General Relativity, 1995
- On the convergence of Regge calculus to general relativity, 2000
The question of consistency is a purely mathematical one, and therefore I do not expect it to be "debatable". I will have to work with this theory and hence I do wonder in how far there is a theoretical basis to tell apart "It works" and "It does not work".
Thank you very much!