an encyclopedia of finite element definitions

# Regge

 Orders $$1\leqslant k$$ Reference elements triangle, tetrahedron Polynomial set $$\mathcal{Z}^{(2)}_{k}$$↓ Show polynomial set definitions ↓ DOFs On each edge: point evaluations of inner products with direction of edge On each face: point evaluations of inner products with direction of edges On each volume: point evaluations of inner products with direction of edges Number of DOFs triangle: $$3(k+1)(k+2)/2$$ (A045943)tetrahedron: $$(k+1)(k+2)(k+3)$$ (A007531) Mapping double covariant Piola continuity Inner products with tangents to facets are continuous Categories Matrix-valued elements

## Implementations

 Basix basix.ElementFamily.Regge↓ Show Basix examples ↓ This implementation is incorrect for this element. Basix.UFL basix.ElementFamily.Regge↓ Show Basix.UFL examples ↓ This implementation is incorrect for this element. FIAT FIAT.Regge↓ Show FIAT examples ↓ This implementation is correct for all the examples below. Symfem "Regge"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations. (legacy) UFL "Regge"↓ Show (legacy) UFL examples ↓

## Examples

 triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions)
• Regge, Tullio. General relativity without coordinates, Il Nuovo Cimento 19(3), 558–571, 1961. [DOI: 10.1007/BF02733251] [BibTeX]
• Christiansen, Snorre H. On the linearization of Regge calculus, Numerische Mathematik 119(4), 613–640, 2011. [DOI: 10.1007/s00211-011-0394-z] [BibTeX]

## DefElement stats

 Element added 01 January 2021 Element last updated 16 September 2023