an encyclopedia of finite element definitions

# Bubble

 Orders interval: $$2\leqslant k$$ triangle: $$3\leqslant k$$ tetrahedron: $$4\leqslant k$$ Reference elements interval, triangle, tetrahedron Polynomial set $$\mathcal{Z}^{(11)}_{k}$$↓ Show polynomial set definitions ↓ DOFs On the interior of the reference element: point evaluations Number of DOFs interval: $$k-1$$ (A000027)triangle: $$(k-2)(k-1)/2$$ (A000217)tetrahedron: $$(k-3)(k-2)(k-1)/6$$ (A000292) Mapping identity continuity Function values are continuous. Categories Scalar-valued elements

## Implementations

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

## Examples

 intervalorder 2 (click to view basis functions) intervalorder 3 (click to view basis functions) triangleorder 3 (click to view basis functions) triangleorder 4 (click to view basis functions)
• Kirby, Robert C., Logg, Anders, Rognes, Marie E., and Terrel, Andy R. Common and unusual finite elements, in Automated solution of differential equations by the finite element method (eds: Logg, Anders, Mardal, Kent-Andre, and Wells, Garth N.), 2012. [DOI: 10.1007/978-3-642-23099-8_3] [BibTeX]

## DefElement stats

 Element added 10 January 2021 Element last updated 16 September 2023