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

.. py:module:: symfem.elements.serendipity

.. autoapi-nested-parse::

   Serendipity elements on tensor product cells.

   This element's definition appears in https://doi.org/10.1007/s10208-011-9087-3
   (Arnold, Awanou, 2011)



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

Classes
~~~~~~~

.. autoapisummary::

   symfem.elements.serendipity.Serendipity
   symfem.elements.serendipity.SerendipityCurl
   symfem.elements.serendipity.SerendipityDiv




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


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

   A serendipity element.

   .. py:attribute:: names
      :value: ['serendipity', 'S']

      

   .. py:attribute:: references
      :value: ['interval', '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:: SerendipityCurl(reference: symfem.references.Reference, order: int, variant: str = 'equispaced')


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

   A serendipity Hcurl element.

   .. py:attribute:: names
      :value: ['serendipity Hcurl', 'Scurl', 'BDMCE', 'AAE']

      

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

      

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

      

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

      

   .. py:attribute:: last_updated
      :value: '2023.07'

      

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

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary



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


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

   A serendipity Hdiv element.

   .. py:attribute:: names
      :value: ['serendipity Hdiv', 'Sdiv', 'BDMCF', 'AAF']

      

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

      

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

      

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

      

   .. py:attribute:: last_updated
      :value: '2023.07'

      

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

      Return the kwargs used to create this element.

      :returns: Keyword argument dictionary