Mathematics of Computation· 2026Q1
Finite elements for symmetric and traceless tensors in three dimensions
- 2citations
- Q1SCImago
- 2026year
Short summary
A new family of finite element sub-complexes for tetrahedral meshes enables exact discrete representations of transverse traceless tensors, crucial for continuum mechanics and general relativity.
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Key points
- Developed finite element sub-complexes for tetrahedral meshes, proving their exactness on contractible domains.
- Included vector fields and symmetric, traceless tensor fields connected via conformal Killing, linearized Cotton-York, and divergence operators.
- Enables discrete representations of transverse traceless tensors (symmetric, traceless, divergence-free) for continuum mechanics and general relativity.
- Demonstrated inf-sup stability for H(div)-conforming finite element symmetric and traceless tensors paired with discontinuous vectors.
AI-generated from the title and abstract; the full text is not read.
Abstract
We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector fields and symmetric and traceless tensor fields, connected through the conformal Killing operator, the linearized Cotton-York operator, and the divergence operator, respectively. This leads to discrete versions of transverse traceless tensors, i.e., symmetric, traceless and divergence-free matrix fields, in continuum mechanics and general relativity. We also show the inf-sup stability of the H ( div ) H(\operatorname {div}) -conforming finite element symmetric and traceless tensors paired with discontinuous vectors.
The authors' abstract, as published at the source. Mathematics of Computation, 2026 · DOI ↗
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Field: Nuclear and High Energy Physics
Nuclear and High Energy PhysicsPhysics and Astronomy