DPc

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

Before trying this example, you must install Basix:

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

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

import basix

# Create dPc order 1 on a quadrilateral
element = basix.create_element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 1, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

# Create dPc order 2 on a quadrilateral
element = basix.create_element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 2, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

# Create dPc order 3 on a quadrilateral
element = basix.create_element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 3, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

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 dPc order 1 on a quadrilateral
element = basix.ufl.element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 1, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

# Create dPc order 2 on a quadrilateral
element = basix.ufl.element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 2, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

# Create dPc order 3 on a quadrilateral
element = basix.ufl.element(basix.ElementFamily.DPC, basix.CellType.quadrilateral, 3, dpc_variant=basix.DPCVariant.simplex_equispaced, discontinuous=True)

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 dPc order 1
element = FIAT.DPC(FIAT.ufc_cell("interval"), 1)

# Create dPc order 2
element = FIAT.DPC(FIAT.ufc_cell("interval"), 2)

# Create dPc order 3
element = FIAT.DPC(FIAT.ufc_cell("interval"), 3)

# Create dPc order 1
element = FIAT.DPC(FIAT.reference_element.UFCQuadrilateral(), 1)

# Create dPc order 2
element = FIAT.DPC(FIAT.reference_element.UFCQuadrilateral(), 2)

# Create dPc order 3
element = FIAT.DPC(FIAT.reference_element.UFCQuadrilateral(), 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 dPc order 1 on a interval
element = symfem.create_element("interval", "dPc", 1)

# Create dPc order 2 on a interval
element = symfem.create_element("interval", "dPc", 2)

# Create dPc order 3 on a interval
element = symfem.create_element("interval", "dPc", 3)

# Create dPc order 1 on a quadrilateral
element = symfem.create_element("quadrilateral", "dPc", 1)

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

# Create dPc order 3 on a quadrilateral
element = symfem.create_element("quadrilateral", "dPc", 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 dPc order 1 on a interval
element = ufl_legacy.FiniteElement("DPC", "interval", 1)

# Create dPc order 2 on a interval
element = ufl_legacy.FiniteElement("DPC", "interval", 2)

# Create dPc order 3 on a interval
element = ufl_legacy.FiniteElement("DPC", "interval", 3)

# Create dPc order 1 on a quadrilateral
element = ufl_legacy.FiniteElement("DPC", "quadrilateral", 1)

# Create dPc order 2 on a quadrilateral
element = ufl_legacy.FiniteElement("DPC", "quadrilateral", 2)

# Create dPc order 3 on a quadrilateral
element = ufl_legacy.FiniteElement("DPC", "quadrilateral", 3)