[Dune] Available quadrature orders?

[Christian Engwer]

Dear Aleksejs,

I recommend the dune-grid-howto. It contains a PDF and example
programe. One of them explains how to implement a simple FEM problem
and in this course it also explains how to use the QuadratureRules.

Christian

On Fri, Mar 06, 2015 at 09:27:02AM +0100, Aleksejs Fomins wrote:
> 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
> 
> _______________________________________________
> Dune mailing list
> Dune at dune-project.org
> http://lists.dune-project.org/mailman/listinfo/dune
> 

-- 
Prof. Dr. Christian Engwer 
Institut für Numerische und Angewandte Mathematik
Fachbereich Mathematik und Informatik der Universität Münster
Einsteinstrasse 62
48149 Münster

E-Mail	christian.engwer at uni-muenster.de
Telefon	+49 251 83-35067
FAX		+49 251 83-32729