an encyclopedia of finite element definitions

# Wu–Xu

 Orders interval: $$k=2$$ triangle: $$k=3$$ tetrahedron: $$k=4$$ Reference elements interval, triangle, tetrahedron Polynomial set $$\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(53)}_{k}$$ (interval) $$\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(54)}_{k}$$ (triangle) $$\mathcal{P}_{k-1} \oplus \mathcal{Z}^{(55)}_{k}$$ (tetrahedron) ↓ Show polynomial set definitions ↓ DOFs On each vertex: point evaluations On each edge: integrals of normal derivatives On each face: integrals of normal derivatives On each volume: integrals of normal derivatives Number of DOFs interval: $$4$$triangle: $$12$$tetrahedron: $$38$$ Mapping identity continuity Function values are continuous. Categories Scalar-valued elements

## Implementations

 Symfem "Wu-Xu"↓ Show Symfem examples ↓ This implementation is used to compute the examples below and verify other implementations.

## Examples

 intervalorder 2 (click to view basis functions) triangleorder 3 (click to view basis functions) tetrahedronorder 4 (click to view basis functions)
• Wu, Shuonan and Xu, Jinchao. Nonconforming finite element spaces for 2mth order partial differential equations on Rn simplical grids when m=n+1, Mathematics of computation 88, 531–551, 2019. [DOI: 10.1090/mcom/3361] [BibTeX]

## DefElement stats

 Element added 08 June 2021 Element last updated 16 September 2023