ffc team mailing list archive

[Marie Rognes <meg@xxxxxxxxx>]

Andy Ray Terrel wrote:
> Okay I see.  Its just a third order bubble, sometimes I send mail
> before I think.  The mini element is a first order bubble or at least
> that's what Brezzi Fortin say.
>
>   

That depends on your definition of the word "is".

The "velocity" part of the (lowest order) Mini element is, in FFC:
  
   P1 = VectorElement("Lagrange", triangle, 1)
   B = VectorElement("Bubble", triangle, 3)
   V = P1 + B


The logic here is that the degree should be such that any element
of degree k is included in P_k. Hence, for triangles, the numbering for the
bubbles start at 3.

--
Marie

> -- Andy
>
>
>
> On Fri, Apr 9, 2010 at 8:43 PM,  <meg@xxxxxxxxx> wrote:
>   
> > > Is there anything telling how the bubble functions are defined?
> > >
> > > For example with the Mini example:
> > >
> > > P1 = VectorElement("Lagrange", "triangle", 1)
> > > B = VectorElement("Bubble", "triangle", 3)
> > > Q = FiniteElement("Lagrange", "triangle", 1)
> > > Mini = (P1 + B) * Q
> > >
> > > Does B consist of 3 bubble functions in some symmetric pattern in the
> > > element?
> > >
> > >       
> > The bubble functions are the bubble functions ;)
> >
> > In the above example, B is the span of the piecewise continuous
> > cubic functions that are zero on the boundary of each triangle.
> > (1 per triangle for a FiniteElement and hence 2 per triangle for a
> > VectorElement of value dimension 2.)
> >
> > In general, the bubble finite element of degree k is the span of the interior
> > basis functions of CG_k.
> >
> > --
> > Marie
> >
> >
> >
> >