symfem.elements.hct

Hsieh-Clough-Tocher elements on simplices.

This element’s definition appears in https://doi.org/10.2307/2006147 (Ciarlet, 1978)

Classes

HsiehCloughTocher

Hsieh-Clough-Tocher finite element.

Module Contents

class symfem.elements.hct.HsiehCloughTocher(reference: symfem.references.Reference, order: int)

Bases: symfem.finite_element.CiarletElement

Hsieh-Clough-Tocher finite element.

property lagrange_subdegree: int

Abstractmethod:

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

Abstractmethod:

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

Abstractmethod:

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

Abstractmethod:

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 = ['Hsieh-Clough-Tocher', 'Clough-Tocher', 'HCT', 'CT']

references = ['triangle']

min_order = 3

max_order = 3

continuity = 'C0'

value_type = 'scalar macro'

last_updated = '2025.12'