[Dune] Local p-refinement in DUNE?

[Bryan Doyle]

Hello Christian,
Thank you for your response! Having a non-conforming FEM is not an issue
for me at this point, so I have been looking into the variableqkdgfem.hh
implementation as per your suggestion, and think that this is exactly what
I was looking for.

However, I had a follow-up question I was hoping to get feedback on: on
line 24 of variableqkdgfem.hh, "Dune::QkDGLocalFiniteElement" is called,
and my compiler complains that this does not name a template type. Should
this be defined for me somewhere in dune/localfunctions/, where classes
like "QkLocalFiniteElement" and "PkLocalFiniteElement" are defined? I don't
see this anywhere in my code (I am using v2.5.1), so I was curious if I am
missing some file or if I have to define the class "QkDGLocalFiniteElement"
myself. I appreciate any feedback you or anyone else may have!

Thank you for your time,
Bryan

On Thu, Mar 22, 2018 at 2:15 PM, Christian Engwer <christian.engwer at uni-
muenster.de> wrote:

> Dear Bryan,
>
> there is a limited amount of support for p-refinement. There are
> different variable*fem.hh implementations of DG bases with variable
> polynomial degree. You can specify the degree via a non-standard
> method
>       void setOrder (const EntityType& e, unsigned int p)
>
> This should work quite straight forward. If you want to use conforming
> FEM things are a bit more complicated. You could implement something
> very similar to the current implementation, but how do you ensure
> conformity. This has to be done either by the finite-element-map by
> providing a specific finite-element which has a lower degree on a
> face, or by introducing appropriate constraints. Currently
> dune-localfunctions is not able to create such mixed degree elements
> and I don't think this is a viable apporach. So you want the
> constraints... PDELab has a couple of constraints implementations, but
> non that will work for this case.
>
> So first question is ... what exactly do you need?
>
> Best
> Christian
>
>
> > Hello,
> > I am attempting to implement the ability to locally refine the polynomial
> > degree of the function space within my DUNE code, using PDELab. My first
> > thought was to use DUNE's "CompositeGridFunction" functionality, but I do
> > not believe this allows for modification of the grid space degree across
> > the domain.
> >
> > To do this, would I instead have to code my own finite-element map whose
> > degree changes across the domain, and make a grid function space out of
> > that? Are there any tutorials available where such refinement is done? I
> > don't have any ideas of a starting point, so any thoughts or pointers
> would
> > be greatly appreciated!
> >
> > Thank you,
> > Bryan
>
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