Bastien, as there already is the Polynomial class HermiteInterpolation you should create a new FiniteElement based on a TensorProductPolynomial<HermiteInterpolation>. A good way might be to copy FE_Q_Base and modify it accordingly. Of course you need to think about how to interpolate values using this element, how to use constraints, etc. You don't need to implement everything (like restriction and interpolation matrices) immediately. If you are interested, just start and ask when you're stuck.
Best, Daniel Am Montag, 6. Juni 2016 20:04:04 UTC+2 schrieb Bastien Lauras: > > Dear Guido and dear all, > > I am trying to implement Hermitian Cubic elements on a 1D beam. I am > working on the vertical displacement y of the beam (only displacement > allowed, the beam is inextensible). I need a continuous first derivative of > the displacement, and this can easily be done with Hermitian Cubic elements. > But I don't understand well the Polynomial module. I've seen that Hermite > Interpolation > <https://dealii.org/developer/doxygen/deal.II/classPolynomials_1_1HermiteInterpolation.html> > exists > in deal.II. Though, I don't understand how I can define a polynomial space, > so that FE_Q would work with my Hermitian elements and not Lagrangian > elements. > > Thanks a lot for your help! > > Best, > > Bastien > > On Thursday, September 27, 2012 at 7:33:20 AM UTC-5, Guido Kanschat wrote: >> >> Dear Nicola, >> >> typically, we define finite element shape function spaces in two steps: >> >> 1. Define a polynomial space. Here, you can find examples in the >> module on Polynomials, in particular classes like >> TensorProductPolynomials or PolynomialsBDM. Your task would >> essentially be adding an additional constant function to >> TensorProductPolynomials. >> >> 2. Create a finite element using your new polynomial space. FE_Q would >> be your model here. Unfortunately, FE_Q has a lot of complicated >> hidden logic like the renumbering of polynomials from tensor product >> structure to internal deal.II enumeration. You would have to make >> sure, that your new polynomial at the end of the list stays at the >> end, since it is located in the interior of the cell. >> >> I can help with the implementation if you get it started. >> >> Best, >> Guido >> > -- 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 dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
