[Dune] Available quadrature orders?

[Oliver Sander]

> 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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