Vector Lagrange

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

Before trying this example, you must install Symfem:

pip3 install symfem

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

import symfem

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

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

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

# Create vector Lagrange order 2 on a tetrahedron
element = symfem.create_element("tetrahedron", "vector Lagrange", 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 Lagrange order 1 on a triangle
element = ufl.VectorElement("Lagrange", "triangle", 1)

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

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

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