[Dune] [#723] method order on basis

[Dune]

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A new Flyspray task has been opened.  Details are below. 

User who did this - Andreas Dedner (dedner) 

Attached to Project - Dune
Summary - method order on basis
Task Type - Bug Report
Category - Localfunctions
Status - New
Assigned To - 
Operating System - Unspecified / All
Severity - High
Priority - High
Reported Version - SVN (pre2.0)
Due in Version - Undecided
Due Date - Undecided
Details - What is the exact semantics of order()?

We would suggest to have two methods:
k=interpolationOrder(): P_k subset span<b_i>
K=maxOrder():           span<b_i> subset P_K
Example: RT_0 would have k=0, K=1
         Q_p  would have k=p, K=2p
         P_p  would have k=K=p
Note that the maxOrder is only meaningful for polynomial
basis functions (e.g. a sin/cos basis would have to have
k=0, K=infinity).

A third value which might be even more practical, is a bit
difficult to define and has something todo with the required
quadrature order. Assuming e.g. that a tensor product
quadrature is used on cubes then the quadrature order for
Q_p would be p=interpolationOrder();
but for RT_0 on simplex elements we need order 1=maxOrder().
Of course maxOrder always works but in the case of Q_p it
is much to large.

At the moment the order seems not consistently implemented:
Q1LocalBasis::order returns 1 (interpolation order)
RT0LocalBasis::order returns 1 (max order)
Our basis function return the ''quadrature order''.


More information can be found at the following URL:
http://www.dune-project.org/flyspray/index.php?do=details&task_id=723

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