Re: [Ffc] Bubble function
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, 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
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Re: [Ffc] Bubble function
Okay so Brezzi Fortin have just a bubble function with one node. Perhaps they meant P3 but their notation is ambiguous. ArnoldBrezziFortin1984 does call for the P3 in the original paper but then they mention using 2 P4 bubble functions for the next velocity order. If I do enrich with 2 P4 bubbles with ffc will the bubble functions be any different. It just seems like it will give exactly the same evaluation points as enriching with 1 bubble function. -- Andy ___ Mailing list: https://launchpad.net/~ffc Post to : ffc@lists.launchpad.net Unsubscribe : https://launchpad.net/~ffc More help : https://help.launchpad.net/ListHelp
Re: [Ffc] Bubble function
Andy Ray Terrel wrote: Okay so Brezzi Fortin have just a bubble function with one node. Perhaps they meant P3 but their notation is ambiguous. ArnoldBrezziFortin1984 does call for the P3 in the original paper but then they mention using 2 P4 bubble functions for the next velocity order. If I do enrich with 2 P4 bubbles with ffc will the bubble functions be any different. It just seems like it will give exactly the same evaluation points as enriching with 1 bubble function. I'm not quite sure what you mean by enriching with 2 P4 bubble functions. Do you mean 2 as in 2 components? Note that the bubble space of degree 4 has local dimension 3. Are you sure that you have the latest ffc? -- Marie ___ Mailing list: https://launchpad.net/~ffc Post to : ffc@lists.launchpad.net Unsubscribe : https://launchpad.net/~ffc More help : https://help.launchpad.net/ListHelp
