Bell

\(\mathcal{Z}^{(4)}_k=\left\{p\in\mathcal{P}_{k}\middle|\text{normal derivative of $p$ on each edge is cubic}\right\}\)

\(\mathcal{P}_k=\operatorname{span}\left\{\prod_{i=1}^dx_i^{p_i}\middle|\sum_{i=1}^dp_i\leqslant k\right\}\)

Before trying this example, you must install FIAT:

pip3 install git+https://github.com/firedrakeproject/fiat.git

This element can then be created with the following lines of Python:

import FIAT

# Create Bell order 5
element = FIAT.Bell(FIAT.ufc_cell("triangle"))

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 Bell order 5 on a triangle
element = symfem.create_element("triangle", "Bell", 5)

Before trying this example, you must install (legacy) UFL:

pip3 install fenics-ufl-legacy

This element can then be created with the following lines of Python:

import ufl_legacy

# Create Bell order 5 on a triangle
element = ufl_legacy.FiniteElement("Bell", "triangle", 5)