symfem.elements.mtw

Mardal-Tai-Winther elements on simplices.

This element’s definition appears in https://doi.org/10.1137/S0036142901383910 (Mardal, Tai, Winther, 2002) and https://doi.org/10.1007/s10092-006-0124-6 (Tail, Mardal, 2006)

Classes

MardalTaiWinther

Mardal-Tai-Winther Hdiv finite element.

Module Contents

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

Bases: symfem.finite_element.CiarletElement

Mardal-Tai-Winther Hdiv 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 = ['Mardal-Tai-Winther', 'MTW']

references = ['triangle', 'tetrahedron']

min_order = 1

max_order = 1

continuity = 'H(div)'

value_type = 'vector'

last_updated = '2025.12'