symfem.elements.crouzeix_raviart

Crouzeix-Raviart elements on simplices.

This element’s definition appears in https://doi.org/10.1051/m2an/197307R300331 (Crouzeix, Raviart, 1973)

Classes

CrouzeixRaviart

Crouzeix-Raviart finite element.

Module Contents

class symfem.elements.crouzeix_raviart.CrouzeixRaviart(reference: symfem.references.Reference, order: int, variant: str = 'equispaced')

Bases: symfem.finite_element.CiarletElement

Crouzeix-Raviart finite element.

variant = 'equispaced'

init_kwargs() → dict[str, Any]

Return the kwargs used to create this element.

Returns:

Keyword argument dictionary

property lagrange_subdegree: int

Get the Lagrange subdegree of the element.

This is the degree of the highest degree Lagrange space whose polynomial space is a subspace of this element’s polynomial space.

property lagrange_superdegree: int | None

Get the Lagrange superdegree of the element.

This is the degree of the highest degree Lagrange space whose polynomial space is a superspace of this element’s polynomial space.

property polynomial_subdegree: int

Get the polynomial subdegree of the element.

This is the degree of the highest degree complete polynomial space that is a subspace of this element’s polynomial space.

property polynomial_superdegree: int | None

Get the polynomial superdegree of the element.

This is the degree of the highest degree complete polynomial space that is a superspace of this element’s polynomial space.

names = ['Crouzeix-Raviart', 'CR', 'Crouzeix-Falk', 'CF']

references = ['triangle', 'tetrahedron']

min_order = 1

max_order

continuity = 'L2'

value_type = 'scalar'

last_updated = '2025.12'