[Dune] [#182] P2 shape functions for prism and pyramid are missing

Dune flyspray at dune-project.org
Thu Sep 8 17:16:34 CEST 2011


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The following task has a new comment added:

FS#182 - P2 shape functions for prism and pyramid are missing
User who did this - Bernd Flemisch (Bernd)

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I guess that this is still open? 

It would be great to have a consistent set of quadratic continuous FEs for 3d grids with mixed geometry types. I guess that such a consistent set should be put together in pqkfactory.hh?

As far as I see it, we now have: 
P2 for tets, Q2 for hexas, + a 18 dof something for prisms. 
I would go ahead and implement a corresponding 14 dof something for pyramids, as the one given in 
www.global-sci.org/aamm/freedownload/32-131.pdf

There is also another option: 
P2 for tets, Serendipity for hexas, 15 dof-prisms, 13 dof-pyramids. 
This has been implemented in UG, and explained in a 1997 paper by C. Wieners. It usually has the same qualitative properties as the full approach above, but dofs are only associated with vertices and edges of the mesh, one saves the dofs for faces and interiors. Maybe at some point, this could also be implemented. 

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