Dear all,
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? 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.
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. I hope
the bubble function only provides a local support to estimate the
stabilization parameter but not involved into the global linear system. How
can I deactive the dofs of bubble function when I distributed the dofs like
dof_handler.distribute_dofs(fe) in the tutorial.
I am pretty new with dealii. Any clue or reference paper is fine.
Thanks you guys in advance.
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