:py:mod:`symfem.elements.tnt`
=============================

.. py:module:: symfem.elements.tnt

.. autoapi-nested-parse::

   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
~~~~~~~

.. autoapisummary::

   symfem.elements.tnt.TNT
   symfem.elements.tnt.TNTcurl
   symfem.elements.tnt.TNTdiv



Functions
~~~~~~~~~

.. autoapisummary::

   symfem.elements.tnt.p
   symfem.elements.tnt.b



.. py:function:: p(k: int, v: sympy.core.symbol.Symbol) -> symfem.functions.ScalarFunction

   Return the kth Legendre polynomial.

   :param k: k
   :param v: The variable to use

   :returns: The kth Legendre polynomial


.. py:function:: 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).

   :param k: k
   :param v: The variable to use

   :returns: The function B_k


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


   Bases: :py:obj:`symfem.finite_element.CiarletElement`

   TiNiest Tensor scalar finite element.

   .. py:attribute:: names
      :value: ['tiniest tensor', 'TNT']

      

   .. py:attribute:: references
      :value: ['quadrilateral', 'hexahedron']

      

   .. py:attribute:: min_order
      :value: 1

      

   .. py:attribute:: continuity
      :value: 'C0'

      

   .. py:attribute:: last_updated
      :value: '2023.06'

      

   .. py:method:: init_kwargs() -> Dict[str, Any]

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary



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


   Bases: :py:obj:`symfem.finite_element.CiarletElement`

   TiNiest Tensor Hcurl finite element.

   .. py:attribute:: names
      :value: ['tiniest tensor Hcurl', 'TNTcurl']

      

   .. py:attribute:: references
      :value: ['quadrilateral', 'hexahedron']

      

   .. py:attribute:: min_order
      :value: 1

      

   .. py:attribute:: continuity
      :value: 'H(curl)'

      

   .. py:attribute:: last_updated
      :value: '2023.06'

      

   .. py:method:: init_kwargs() -> Dict[str, Any]

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary



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


   Bases: :py:obj:`symfem.finite_element.CiarletElement`

   TiNiest Tensor Hdiv finite element.

   .. py:attribute:: names
      :value: ['tiniest tensor Hdiv', 'TNTdiv']

      

   .. py:attribute:: references
      :value: ['quadrilateral', 'hexahedron']

      

   .. py:attribute:: min_order
      :value: 1

      

   .. py:attribute:: continuity
      :value: 'H(div)'

      

   .. py:attribute:: last_updated
      :value: '2023.06'

      

   .. py:method:: init_kwargs() -> Dict[str, Any]

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary