Bubble
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Orders | interval: \(2\leqslant k\)
triangle: \(3\leqslant k\)
tetrahedron: \(4\leqslant k\) |
Reference elements | interval, triangle, tetrahedron |
Polynomial set | \(\mathcal{Z}^{(10)}_{k}\) ↓ Show polynomial set definitions ↓↑ Hide polynomial set definitions ↑\(\mathcal{Z}^{(10)}_k=\left\{p\in \mathcal{P}_{k}\middle|p=0\text{ on the boundary}\right\}\)
\(\mathcal{P}_k=\operatorname{span}\left\{\prod_{i=1}^dx_i^{p_i}\middle|\sum_{i=1}^dp_i\leqslant k\right\}\) |
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 ↓↑ Hide Basix examples ↑Before trying this example, you must install Basix: pip3 install git+https://github.com/fenics/basix.git This element can then be created with the following lines of Python: import basix
# Create bubble order 2 on a interval element = basix.create_element(basix.ElementFamily.bubble, basix.CellType.interval, 2)
# Create bubble order 3 on a interval element = basix.create_element(basix.ElementFamily.bubble, basix.CellType.interval, 3)
# Create bubble order 3 on a triangle element = basix.create_element(basix.ElementFamily.bubble, basix.CellType.triangle, 3)
# Create bubble order 4 on a triangle element = basix.create_element(basix.ElementFamily.bubble, basix.CellType.triangle, 4) |
Symfem | "bubble" ↓ Show Symfem examples ↓↑ Hide Symfem examples ↑Before trying this example, you must install Symfem: pip3 install symfem This element can then be created with the following lines of Python: import symfem
# Create bubble order 2 on a interval element = symfem.create_element("interval", "bubble", 2)
# Create bubble order 3 on a interval element = symfem.create_element("interval", "bubble", 3)
# Create bubble order 3 on a triangle element = symfem.create_element("triangle", "bubble", 3)
# Create bubble order 4 on a triangle element = symfem.create_element("triangle", "bubble", 4) |
UFL | "Bubble" ↓ Show UFL examples ↓↑ Hide UFL examples ↑Before trying this example, you must install UFL: pip3 install UFL This element can then be created with the following lines of Python: import ufl
# Create bubble order 2 on a interval element = ufl.FiniteElement("Bubble", "interval", 2)
# Create bubble order 3 on a interval element = ufl.FiniteElement("Bubble", "interval", 3)
# Create bubble order 3 on a triangle element = ufl.FiniteElement("Bubble", "triangle", 3)
# Create bubble order 4 on a triangle element = ufl.FiniteElement("Bubble", "triangle", 4) |
Examples
References
- 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 | 02 August 2022 |