symfem.elements.abf

Arnold-Boffi-Falk elements on quadrilaterals.

Thse elements definitions appear in https://dx.doi.org/10.1137/S0036142903431924 (Arnold, Boffi, Falk, 2005)

Classes

ArnoldBoffiFalk

An Arnold-Boffi-Falk element.

Module Contents

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

Bases: symfem.finite_element.CiarletElement

An Arnold-Boffi-Falk 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 = ['Arnold-Boffi-Falk', 'ABF']

references = ['quadrilateral']

min_order = 0

continuity = 'H(div)'

value_type = 'vector'

last_updated = '2025.03'