an encyclopedia of finite element definitions

# Morley–Wang–Xu

 Orders $$1\leqslant k\leqslant {'interval': 1, 'triangle': 2, 'tetrahedron': 3}$$ Reference elements interval, triangle, tetrahedron Polynomial set $$\mathcal{P}_{k}$$↓ 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: $$k+1$$ (A000027)triangle: $$(k+1)(k+2)/2$$ (A000217)tetrahedron: $$(k+1)(k+2)(k+3)/6$$ (A000292) Mapping identity Categories Scalar-valued elements

## Implementations

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

## Examples

 intervalorder 1 (click to view basis functions) triangleorder 1 (click to view basis functions) triangleorder 2 (click to view basis functions) tetrahedronorder 1 (click to view basis functions) tetrahedronorder 2 (click to view basis functions) tetrahedronorder 3 (click to view basis functions)
• Wang, Ming and Xu, Jaochao. Minimal finite element spaces for 2m-th-order partial differential equations in Rn, Mathematics of computation 82(281), 25–43, 2013. [DOI: 10.1090/S0025-5718-2012-02611-1] [BibTeX]

## DefElement stats

 Element added 08 June 2021 Element last updated 16 September 2023