On 8/4/19 5:47 PM, Jonathan Russ wrote:
>
> Thank you for your reply. The shape functions of the "quadratic" serendipity
> elements are very similar to the FE_Q(2) elements except they are derived
> without any interior nodes (i.e. in 2D the interior node is removed and the
> shape functions are simple polynomials with 8 undetermined coefficients
> instead of 9 as with a normal quadratic Lagrange element. Essentially the
> polynomials are not quadratic complete since they are missing the x^2 * y^2
> term). It's pretty simple to express them in 2D and 3D for the "quadratic"
> case (I put quadratic in quotes since the polynomials are not quadratic
> complete) but I am more worried about how difficult it would be to get this
> type of element to work with all of the other functionality in dealii (e.g.
> the DoFHandler, Triangulation, grid refinement, etc.). Do you have a sense
> for
> whether this requires a significant amount of additional effort?
A month at most. Maybe less.
There are many examples of elements already implemented. The easiest way to do
things is if you have a description of the polynomial space in some way. Take
a look at the FE_Poly class and how it is used in some of the other classes.
Depending on how you describe the serendipity space, this may be almost
everything you actually need -- or maybe there are more complications.
The FE interface is very self contained. You won't have to touch the
DoFHandler or any other class. All you have to describe are the shape
functions, what kind of continuity you have across faces and vertices, how
hanging nodes look like (likely the same as the FE_Q(2)), and a few small
other pieces of information that one can often ignore at first.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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