symfem.elements.trimmed_serendipity¶

Trimmed serendipity elements on tensor products.

These elements’ definitions appear in https://doi.org/10.1137/16M1073352 (Cockburn, Fu, 2017) and https://doi.org/10.1090/mcom/3354 (Gilette, Kloefkorn, 2018)

Classes¶

`TrimmedSerendipityHcurl`	Trimmed serendipity Hcurl finite element.
`TrimmedSerendipityHdiv`	Trimmed serendipity Hdiv finite element.

Module Contents¶

class symfem.elements.trimmed_serendipity.TrimmedSerendipityHcurl(reference: symfem.references.Reference, order: int, variant: str = 'equispaced')¶

Bases: symfem.finite_element.CiarletElement

Trimmed serendipity Hcurl 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 = ['trimmed serendipity Hcurl', 'TScurl']¶

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

min_order = 0¶

continuity = 'H(curl)'¶

value_type = 'vector'¶

last_updated = '2025.10'¶

class symfem.elements.trimmed_serendipity.TrimmedSerendipityHdiv(reference: symfem.references.Reference, order: int, variant: str = 'equispaced')¶