A Vector-Valued Co-Chain/Chain Complex Associated to the Elasticity Complex

Abstract

In this report, we recall Christiansen's [2011, Num. Math.] discrete elasticity complex that uses spaces of polynomials and distributions. Using the degrees of freedom of those spaces, we write a complex using vector-valued chains and co-chains that is isomorphic to Christiansen's complex. The operators of the new complex are algebraic, but use the geometry of the simplicial complex. Finally, we define a de Rham-like map from the smooth elasticity complex to this discrete complex.