[Dune] [#723] method order on basis

Dune flyspray at dune-project.org
Sun Jan 24 21:32:44 CET 2010


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The following task has a new comment added:

FS#723 - method order on basis
User who did this - Carsten Gräser (Carsten)

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The interesting thing is 'the' quadrature order.  This should be the minimal order k such that the quadrature rule returned from dune-grid for k can integrate the basis functions exactly. If the corresponding rule is a tensor product rule it should be p for Q_p. If not it should be as high as needed.

However returning one order is not sufficient in general:
1) Either we use the approach suggested above then Q_p might sometimes have p and some times not. Otherwise the rule for p might not be able to integrate exactly.
2) RefinedP* elements need quadrature rules on subtriangles obtained by red refinement.
3) There are elements defined on barycentric refined triangles (Hsieh-Clough-Tocher).
4) For hierarchical basis functions there are different orders for the functions.
5) If QuadRule(k) with k=basis.order() can integrate the basis functions which rule is needed derivatives, products, products of derivatives, ...

In order to really solve the problem we would need to return some struct that contains more information and a mechanism to construct this for derivatives, products,... . Then some kind of factory should return a proper quadrature.

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