Lixing,
I am trying to implement a stabiliazed weak form (e.g. advection-diffusion)
where the stabilization tensor is computed element-wise through a standard
bubble: \Pi(1-x_i^2). It seems that FE_Q_Bubbles should provides all I need,
but here are two things I am not quite clear about,
1. Is the definition of bubble function in FE_Q_Bubbles in [0,1] span or
[-1,1] span?
Everything in deal.II is on the reference cell define as [0,1]^d.
Does it has the standard bubble shape (1 at element center and
vanishes at the edges)? The (2x_j-1)^{p-1} part is a little bit confusing to
me. The bubble function corresponds to linear element in FE_Q_Bubbles is the
standard bubble that I desire, but I am really confusing at the shape of this
expression at higher orders.
For higher orders, you end up with multiple bubble functions, one for each
j=0..dim-1. This wasn't quite clear from the documentation, and I'll submit a
patch later for that.
2. I tried to utilize this class (i.e., FE_Q_Bubbles). One issue is that it
takes the virtual nodes of the bubble function into account of the total DOFs,
which is not the way we prefer in the stabilization method.
But the behavior is correct -- the class describes a finite element *space*
and that space contains the bubble function. I think that what you are trying
to do is to do static elimination of that degree of freedom right away, and
that can be implemented as well but is not the philosophical view we generally
take in deal.II if you select such an element.
The question is what you want the finite element space to be (i) locally, on
every cell, and (ii) globally. There are a number of tutorials that discuss
these sorts of questions. I would encourage you to read through step-61 and
step-51, for example.
Best
WB
--
------------------------------------------------------------------------
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/19b4cd8a-4b6d-2598-fc7c-bb7cff4b03c9%40colostate.edu.
