Mardal–Tai–Winther

\(\mathcal{Z}^{(18)}_k=\left\{\boldsymbol{p}\in\mathcal{P}_{k}^d\middle|\operatorname{div}\boldsymbol{p}\text{ is constant, and }\boldsymbol{p}\cdot\boldsymbol{n}_{e_i}\text{ is linear on each edge }e_i\right\}\)

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

\(\mathcal{Z}^{(19)}_k=\left\{\nabla\times(xyz(1-x-y-z)\boldsymbol{p})\middle|\boldsymbol{p}\in\mathcal{P}_{k}^d\right\}\)

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 Mardal-Tai-Winther order 3
element = FIAT.MardalTaiWinther(FIAT.ufc_cell("triangle"), 3)

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 Mardal-Tai-Winther order 3 on a triangle
element = symfem.create_element("triangle", "MTW", 3)

# Create Mardal-Tai-Winther order 3 on a tetrahedron
element = symfem.create_element("tetrahedron", "MTW", 3)

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 Mardal-Tai-Winther order 3 on a triangle
element = ufl_legacy.FiniteElement("MTW", "triangle", 3)