symfem.elements.kmv

Kong-Mulder-Veldhuizen elements on triangle.

This element’s definition is given in https://doi.org/10.1023/A:1004420829610 (Chin-Joe-Kong, Mulder, Van Veldhuizen, 1999)

Classes

KongMulderVeldhuizen

Kong-Mulder-Veldhuizen finite element.

Functions

kmv_tri_polyset(→ list[symfem.functions.FunctionInput])

Create the polynomial set for a KMV space on a triangle.

kmv_tet_polyset(→ list[symfem.functions.FunctionInput])

Create the polynomial set for a KMV space on a tetrahedron.

Module Contents

symfem.elements.kmv.kmv_tri_polyset(m: int, mf: int) → list[symfem.functions.FunctionInput]

Create the polynomial set for a KMV space on a triangle.

Parameters:

  • m – The parameter m

  • mf – The parameter mf

Returns:

The polynomial set

symfem.elements.kmv.kmv_tet_polyset(m: int, mf: int, mi: int) → list[symfem.functions.FunctionInput]

Create the polynomial set for a KMV space on a tetrahedron.

Parameters:

  • m – The parameter m

  • mf – The parameter mf

  • mi – The parameter mi

Returns:

The polynomial set

class symfem.elements.kmv.KongMulderVeldhuizen(reference: symfem.references.Reference, order: int)

Bases: symfem.finite_element.CiarletElement

Kong-Mulder-Veldhuizen finite element.

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 = ['Kong-Mulder-Veldhuizen', 'KMV']
references = ['triangle', 'tetrahedron']
min_order = 1
continuity = 'C0'
value_type = 'scalar'
last_updated = '2025.12'