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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
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