symfem.elements.serendipity

Serendipity elements on tensor product cells.

This element’s definition appears in https://doi.org/10.1007/s10208-011-9087-3 (Arnold, Awanou, 2011)

Classes

Serendipity	A serendipity element.
SerendipityCurl	A serendipity Hcurl element.
SerendipityDiv	A serendipity Hdiv element.

Module Contents

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

Bases: symfem.finite_element.CiarletElement

A serendipity 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 = ['serendipity', 'S']

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

min_order = 1

continuity = 'C0'

value_type = 'scalar'

last_updated = '2024.09'

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

Bases: symfem.finite_element.CiarletElement

A serendipity Hcurl 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 = ['serendipity Hcurl', 'Scurl', 'BDMCE', 'AAE']

references = ['quadrilateral', 'hexahedron']

min_order = 1

continuity = 'H(curl)'

value_type = 'vector'

last_updated = '2023.07'

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

Bases: symfem.finite_element.CiarletElement

A serendipity Hdiv 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 = ['serendipity Hdiv', 'Sdiv', 'BDMCF', 'AAF']

references = ['quadrilateral', 'hexahedron']

min_order = 1

continuity = 'H(div)'

value_type = 'vector'

last_updated = '2023.07'