Dear Greg,
Just to extend on what Peter said: It should be possible to define
anisotropic degrees in a completely discontinuous finite element, say
FE_DGP or FE_DGQ. In that case, you would derive from `FE_Poly` and
insert an anisotropic polynomial space, doing whatever you think is
appropriate. For elements imposing some continuity, include
FE_FaceP/FE_FaceQ or the regular H1 functions (FE_Q), you can't do that
as Peter said. However, one could work around this by constructing
constraints that constrain the polynomial space of uniform high order in
one of the directions to the lower polynomial degree. It would be a bit
of work to realize this (say 200-400 lines of code to set up the
constraints), but the easiest solution I could come up.
Best,
Martin
On 11.03.23 17:26, Greg Wang wrote:
Hi Peter,
Thanks a lot for the info!
We have recently implemented in deal.II a space-time HDG method for
the advection-diffusion problem on deforming domains. Our analysis
allows the spatial polynomial order p_s to differ from the temporal
one p_t. When p_t = p_s, we just call FE_DGP, FE_FaceP constructors
with nothing extra to do and the rates come out nicely matching the a
priori rates of convergence. And now we are trying to have a p_t = p_s
+1 test case to further validate our analysis, which led to this post.
Best regards,
Greg
On Saturday, March 11, 2023 at 2:20:37 PM UTC peterr...@gmail.com wrote:
Hi Greg,
unfortunately we do not support anisotropic polynomials: we make
the assumption that all faces (of the same type) and lines have
the same number of DoFs. For what do you need such polynomial spaces?
Best,
Peter
On Saturday, 11 March 2023 at 15:05:25 UTC+1 ygre...@gmail.com wrote:
Hi there,
I was wondering if finite elements with anisotropic polynomial
degrees are possible in deal.II. As an example, for a 3D
element, can we construct a tensor product polynomial space of
{1,x,y,z,xy,xz,yz, z^2,xz^2,yz^2}, i.e., order 1 in x- and
y-directions and 2 in z-direction?
I was looking at, for example, constructors of FE_DGQ() class
[1]. The second constructor [2] takes an arbitrary vector of
polynomials to build the tensor product polynomial space. This
is close to what I want but it seems the argument can only be
one-dimensional polynomials, which means equal order on all
dimensions.
Would really appreciate any insights and/or tips!
Best,
Greg
------------------------------------------
[1] https://dealii.org/current/doxygen/deal.II/classFE__DGQ.html
[1]
https://dealii.org/current/doxygen/deal.II/fe__dgq_8cc_source.html#l00100
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