Arnold–Boffi–Falk

\(\mathcal{Z}^{(0)}_k=\left\{\left(\begin{array}{c}x^py^q\\0\end{array}\right)\middle|p\leqslant k+2,q\leqslant k\right\}\)

\(\mathcal{Z}^{(1)}_k=\left\{\left(\begin{array}{c}0\\x^py^q\end{array}\right)\middle|p\leqslant k,q\leqslant k+2\right\}\)

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 Arnold-Boffi-Falk order 0 on a quadrilateral
element = symfem.create_element("quadrilateral", "ABF", 0)

# Create Arnold-Boffi-Falk order 1 on a quadrilateral
element = symfem.create_element("quadrilateral", "ABF", 1)

# Create Arnold-Boffi-Falk order 2 on a quadrilateral
element = symfem.create_element("quadrilateral", "ABF", 2)