Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.23829

Authors: Peña, Jennifer Amador, de Ángel, Sara, Porras, Fernanda

Institution: Yale University

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204262151

Cites:

Cited by:

Related to: