A discrete elasticity complex on three-dimensional Alfeld splits

TL;DR

This paper develops a new finite element elasticity complex on three-dimensional Alfeld splits, linking vector and tensor fields through differential operators, based on algebraic and differential form techniques.

Contribution

It introduces a conforming finite element elasticity complex on Alfeld splits derived from de Rham complexes and smoother finite element differential forms.

Findings

Constructed a conforming elasticity complex on Alfeld splits

Linked vector and tensor fields via differential operators

Provides a new algebraic machinery for elasticity complexes

Abstract

We construct conforming finite element elasticity complexes on the Alfeld splits of tetrahedra. The complex consists of vector fields and symmetric tensor fields, interlinked via the linearized deformation operator, the linearized curvature operator, and the divergence operator, respectively. The construction is based on an algebraic machinery that derives the elasticity complex from de~Rham complexes, and smoother finite element differential forms.