Vector Q

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

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 vector Q order 1 on a quadrilateral
element = symfem.create_element("quadrilateral", "vector Q", 1)

# Create vector Q order 2 on a quadrilateral
element = symfem.create_element("quadrilateral", "vector Q", 2)

# Create vector Q order 1 on a hexahedron
element = symfem.create_element("hexahedron", "vector Q", 1)

# Create vector Q order 2 on a hexahedron
element = symfem.create_element("hexahedron", "vector Q", 2)

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 vector Q order 1 on a quadrilateral
element = ufl.VectorElement("Q", "quadrilateral", 1)

# Create vector Q order 2 on a quadrilateral
element = ufl.VectorElement("Q", "quadrilateral", 2)

# Create vector Q order 1 on a hexahedron
element = ufl.VectorElement("Q", "hexahedron", 1)

# Create vector Q order 2 on a hexahedron
element = ufl.VectorElement("Q", "hexahedron", 2)