[Dune] Quadrature Rule 4 & 5 Identical

Andreas Dedner A.S.Dedner at warwick.ac.uk
Tue Mar 6 11:24:07 CET 2012

Did you mean order 2 and 3 are the same - at least for cubes your output 
does not have order 5...

The question is: what does the order parameter refer to>
1) convergence order of the quadrature?
2) polynomial order for which it is exact?

For Gauss quadratures (in 1D) we have (I hope I have the formula right):
1) m points -> convergence rate 2m
2) m points -> exact for order 2m-1

I think we use definition 2 of order so therefore there is
no Gauss quadrature for the even orders, or more precisely the best 
quadrature rule you can get for order=2m  has m+1 points (in 1D) and 
therefore also has order 2m+1. So for order=2 you need to use 2 points
and thats the same quadrature you get for order=3.

Hope that helps

On 06/03/12 10:05, Alex Evanovic wrote:
> Hi,
> I was just cross-checking quadrature rules of dune (as I had a problem)
> by printing out the weights and points and it looks to me that the
> quadrature rule of order 4 and order 5 are exactly the same. Is this a bug?
> Please find attached my test code (integration.cc) & output (jj.txt).
> Regards,
> Alex
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