symfem.elements.bubble

Bubble elements on simplices.

This element’s definition appears in https://doi.org/10.1007/978-3-642-23099-8_3 (Kirby, Logg, Rognes, Terrel, 2012)

Classes

Bubble	Bubble finite element.
BubbleEnrichedLagrange	Bubble enriched Lagrange element.
BubbleEnrichedVectorLagrange	Bubble enriched Lagrange element.

Module Contents

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

Bases: symfem.finite_element.CiarletElement

Bubble 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 = ['bubble']

references = ['interval', 'triangle', 'tetrahedron', 'quadrilateral', 'hexahedron']

min_order

continuity = 'C0'

value_type = 'scalar'

last_updated = '2025.12'

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

Bases: symfem.finite_element.CiarletElement

Bubble enriched Lagrange 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 = ['bubble enriched Lagrange']

references = ['triangle']

min_order = 1

continuity = 'C0'

value_type = 'scalar'

last_updated = '2025.12'

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

Bases: symfem.finite_element.CiarletElement

Bubble enriched Lagrange 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 = ['bubble enriched vector Lagrange']

references = ['triangle']

min_order = 1

continuity = 'C0'

value_type = 'vector'

last_updated = '2025.12'