[Dune] a question about quadrature rules

[Christian Engwer]

Dear Arya,

> I got to have a question about the quadrature rules implemented in Dune.
> There seems to be something strange in the Dune tutorial. First, according
> to the comments, if one aims to do integration with quadrature order p, the
> rule should be initialized as:
> 
> const Dune::QuadratureRule <ctype ,dim >& rule = Dune::QuadratureRules
> <ctype ,dim >::rule(gt,p);
> 
> However, later for calculation with order two the p value is set to 1.
> Would you explain a little about this?

Please be a bit more specific. Where in the tutorial is this
statement. We need to have a closer look...

> My main question is that if I want to consider only one point for the
> integration (first order quadrature rule), what should I set for the rule
> order? one or zero?

In general the order you specify is the order for which you compute
the exact integral (modulo fp errors). In particular this means that
integrating a first order function you set the rule to 1. The obtained
rule will be the same as for zero order, but this a detail you don't
have to think about.

Ciao

Christian

> 
> Thank you in advance for your help and best regards,
> Arya

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

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