Regge calculus was introduced in 1961 as a coordinate free and discrete analogue of Einstein's theory of gravitation. Yet, in spite of its beautiful geometric features, the bulk of numerical computations in general relativity is, as of today, carried out by other methods. In this talk I will present the main results I have obtained on the numerical analysis of Regge calculus, with the long term goal of building efficient computational procedures for GR. Of particular importance will be the relationship with the differential complex introduced by Arnold and his collaborators, to construct new finite elements for elasticity.