Nonconforming Arnold–Winther

\(\mathcal{Z}^{(22)}_k=\left\{\mathbf{M}\in\mathcal{P}_{k}^{d\times d}\middle|\mathbf{M}^t=\mathbf{M}\text{ and for every edge }\hat{\mathbf{n}}_i^t\mathbf{M}\hat{\mathbf{n}}_i\text{ is linear }\right\}\)

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

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 nonconforming Arnold-Winther order 2
element = FIAT.ArnoldWintherNC(FIAT.ufc_cell("triangle"), 2)

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 nonconforming Arnold-Winther order 2 on a triangle
element = symfem.create_element("triangle", "nonconforming AW", 2)

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 nonconforming Arnold-Winther order 2 on a triangle
element = ufl_legacy.FiniteElement("AWnc", "triangle", 2)