Finite Element Systems for Vector Bundles: Elasticity and Curvature

Abstract We develop a theory of finite element systems, for the purpose discretizing sections vector bundles, in particular those arising elasticity. In presence curvature, we prove discrete Bianchi identity. flat case, de Rham theorem on cohomology groups. check that some known mixed elements stress–displacement formulation elasticity fit our framework. also define, dimension two, first conforming spaces metrics with good linearized corresponding to strain tensors Saint-Venant compatibility conditions. Cochains coefficients rigid motions are given key role relating continuous and complexes.