symfem.elements.tnt

TiNiest Tensor product (TNT) elements.

These elements’ definitions appear in https://doi.org/10.1090/S0025-5718-2013-02729-9 (Cockburn, Qiu, 2013)

Module Contents

Classes

TNT	TiNiest Tensor scalar finite element.
TNTcurl	TiNiest Tensor Hcurl finite element.
TNTdiv	TiNiest Tensor Hdiv finite element.

Functions

p(→ symfem.functions.ScalarFunction)	Return the kth Legendre polynomial.
b(→ symfem.functions.ScalarFunction)	Return the function B_k.

symfem.elements.tnt.p(k: int, v: sympy.core.symbol.Symbol) → symfem.functions.ScalarFunction

Return the kth Legendre polynomial.

Parameters:

• k – k

• v – The variable to use

Returns:

The kth Legendre polynomial

symfem.elements.tnt.b(k: int, v: sympy.core.symbol.Symbol) → symfem.functions.ScalarFunction

Return the function B_k.

This function is defined on page 4 (606) of https://doi.org/10.1090/S0025-5718-2013-02729-9 (Cockburn, Qiu, 2013).

Parameters:

• k – k

• v – The variable to use

Returns:

The function B_k

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

Bases: symfem.finite_element.CiarletElement

TiNiest Tensor scalar finite element.

names = ['tiniest tensor', 'TNT']

references = ['quadrilateral', 'hexahedron']

min_order = 1

continuity = 'C0'

last_updated = '2023.06'

init_kwargs() → Dict[str, Any]

Return the kwargs used to create this element.

Returns:

Keyword argument dictionary

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

Bases: symfem.finite_element.CiarletElement

TiNiest Tensor Hcurl finite element.

names = ['tiniest tensor Hcurl', 'TNTcurl']

references = ['quadrilateral', 'hexahedron']

min_order = 1

continuity = 'H(curl)'

last_updated = '2023.06'

init_kwargs() → Dict[str, Any]

Return the kwargs used to create this element.

Returns:

Keyword argument dictionary

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

Bases: symfem.finite_element.CiarletElement

TiNiest Tensor Hdiv finite element.

names = ['tiniest tensor Hdiv', 'TNTdiv']

references = ['quadrilateral', 'hexahedron']

min_order = 1

continuity = 'H(div)'

last_updated = '2023.06'

init_kwargs() → Dict[str, Any]

Return the kwargs used to create this element.

Returns:

Keyword argument dictionary