Dear Wolfgang, thanks for the kind response. As a starting point, I would need to focus on a scalar field, hence a finite element space for scalar values would be sufficient, but obviously the mid-long term goal is to employ vector-value finite element as well. I will try to have a look to the class FE_DGVector (which should be more flexible in terms of polynomial thanks to the template parameter PolynomialType) and the implementation of FE_RaviartThomas and FE_RT_Bubbles to deal with different polynomial degrees.
Best Il giorno mercoledì 15 maggio 2024 alle 21:00:40 UTC+2 Wolfgang Bangerth ha scritto: > > Giuseppe, > > > I'm writing this post because I would need help to build a "particular" > finite > > element space. Let us suppose to have a scalar field in 2D. I want to > consider > > a family of basis functions along the horizontal direction (e.g. basis > > functions based on Legendre polynomials) and a different family of basis > > functions along the vertical direction (e.g. basis functions based on > Laguerre > > polynomials). Is there some class that can help to implement such a > space? The > > main difference with respect to the "standard" finite elements is that > the > > this space is not simply the tensor product of 1D basis functions. > > > > There is this class FE_DGVector > > < > https://www.dealii.org/current/doxygen/deal.II/classFE__DGVector.html#a1351e60ba12ff8474b93306930a99701>, > > which maybe can help, but I am not fully sure about that. Indeed, another > required feature is the possibility to consider different degrees along the > two directions, as it happens for instance for Raviart-Thomas spaces. The > constructor of Raviart-Thomas polynomials takes in input two different > polynomial degrees (one for normal direction and another one for the > tangetial direction). Is there some general functionality to do something > similar for other polynomials, which can be in principle different along > the two directions, and then pass it to a finite element space? > > There is no easy approach that is already pre-packaged, mostly because > that's > not a common case. Is your finite element scalar or vector-valued? In the > former case, I don't think that there is any example you can base things > on. > You might just have to derive from FiniteElement and implement things by > hand, > perhaps by looking at how classes such as FE_RaviartThomas do things as an > example. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/03f4cc4f-6ace-4821-89b3-e59bcdd4381bn%40googlegroups.com.
