A discrete elasticity complex on three-dimensional Alfeld splits

Snorre H Christiansen; Jay Gopalakrishnan; Johnny  Guzmán; Kaibo Hu

doi:10.1007/s00211-023-01381-9

A discrete elasticity complex on three-dimensional Alfeld splits

Snorre H Christiansen, Jay Gopalakrishnan, Johnny Guzmán, Kaibo Hu

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	159-204
Journal	Numerische Mathematik
Volume	156
Issue number	1
Early online date	30 Nov 2023
DOIs	https://doi.org/10.1007/s00211-023-01381-9
Publication status	Published - 28 Feb 2024

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10.1007/s00211-023-01381-9

A DISCRETE ELASTICITY COMPLEX ON THREE-DIMENSIONAL ALFELD SPLITSAccepted author manuscript, 482 KB

https://arxiv.org/abs/2009.07744

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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.",

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AB - 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.

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JO - Numerische Mathematik

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A discrete elasticity complex on three-dimensional Alfeld splits

Abstract

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