[Dune] Available quadrature orders?

[Aleksejs Fomins]

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Dear Oliver,

Thank you for your response. 

So I have found the file
dune/geometry/quadraturerules/simplexquadrature.hh
In which it is stated that the highest quadrature order for a triangle is 12 and for a tetrahedron is 5. Is this correct? What would you do if you need to integrate a higher order polynomial?

I would gladly read the book you have sent. Do you happen to have a digital version? I've found it on amazon for $148, but that is a bit too much I think, ignoring the fact that it is in US :)

Regards,
Aleksejs




On 06/03/15 09:55, Oliver Sander wrote:
>> 1) Does Dune possess only 1D quadrature rules, or 2D and 3D also?
> 
> No.  Dune specializes on partial differential equations in one-dimensional domains,
> and therefore only 1d quadrature rules are needed.
> 
>>  I understand that a higher dimensional quadrature can be obtained from a tensor product of lower-dimensional quadratures, but this question is about quadratures specialised for reference element geometries.
>>
>> 2) If yes, for which reference elements, and to what order are these quadrature rules available.
> 
> See dune-geometry/dune/geometry/quadraturerules
> 
>>
>> 3) If no, how does one usually integrate over, say, triangle, using a tensor product quadrature? Does one simply set the value of the function to 0 for all sample points outside the entity? How does that affect the accuracy of integration?
>>
> 
> https://openlibrary.org/books/OL4583400M/Approximate_calculation_of_multiple_integrals
> 
>> 4) Finally, what is known about using quadrature rules for integrating non-polynomial integrands? Can one estimate the quadrature order necessary to integrate, say, sqrt(x) to a given accuracy?
> 
> https://openlibrary.org/books/OL4583400M/Approximate_calculation_of_multiple_integrals
> 
> Cheers,
> Oliver
> 
> 
> 
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