symfem.elements.bddf
====================

.. py:module:: symfem.elements.bddf

.. autoapi-nested-parse::

   Brezzi-Douglas-Duran-Fortin elements.

   This element's definition appears in https://doi.org/10.1007/BF01396752
   (Brezzi, Douglas, Duran, Fortin, 1987)



Classes
-------

.. autoapisummary::

   symfem.elements.bddf.BDDF


Functions
---------

.. autoapisummary::

   symfem.elements.bddf.bddf_polyset


Module Contents
---------------

.. py:function:: bddf_polyset(reference: symfem.references.Reference, order: int) -> list[symfem.functions.FunctionInput]

   Create the polynomial basis for a BDDF element.

   :param reference: The reference cell
   :param order: The polynomial order

   :returns: The polynomial basis


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

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


   Brezzi-Douglas-Duran-Fortin Hdiv finite element.


   .. py:attribute:: variant
      :value: 'equispaced'



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

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary



   .. py:property:: lagrange_subdegree
      :type: 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.


   .. py:property:: lagrange_superdegree
      :type: 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.


   .. py:property:: polynomial_subdegree
      :type: 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.


   .. py:property:: polynomial_superdegree
      :type: 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.


   .. py:attribute:: names
      :value: ['Brezzi-Douglas-Duran-Fortin', 'BDDF']



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



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



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



   .. py:attribute:: value_type
      :value: 'vector'



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