[Dune] Available quadrature orders?

[Aleksejs Fomins]

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Dear Dune,

We have asked this question before, but I do not think we have arrived at a complete understanding of the current state of the art in Dune.

1) Does Dune possess only 1D quadrature rules, or 2D and 3D also? 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.

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?

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?

Regards,
Aleksejs
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