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 Basix.UFL:

pip3 install git+https://github.com/FEniCS/basix.git git+https://github.com/FEniCS/ufl.git

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

import basix
import basix.ufl

# Create vector Lagrange order 1 on a triangle
element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.triangle, 1, lagrange_variant=basix.LagrangeVariant.equispaced, shape=(2,))

# Create vector Lagrange order 2 on a triangle
element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.triangle, 2, lagrange_variant=basix.LagrangeVariant.equispaced, shape=(2,))

# Create vector Lagrange order 1 on a tetrahedron
element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.tetrahedron, 1, lagrange_variant=basix.LagrangeVariant.equispaced, shape=(3,))

# Create vector Lagrange order 2 on a tetrahedron
element = basix.ufl.element(basix.ElementFamily.P, basix.CellType.tetrahedron, 2, lagrange_variant=basix.LagrangeVariant.equispaced, shape=(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 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 (legacy) UFL:

pip3 install fenics-ufl-legacy

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

import ufl_legacy

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

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

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

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