[aspect-devel] matrix assembly

[Wolfgang Bangerth]

On 08/28/2013 02:11 PM, Timo Heister wrote:
>> QGauss<dim>(parameters.composition_degree+2),
>>
>> do we really need such a high order integration scheme?
>
> Normally degree+1 is enough and it should speed up the integration considerably.
> @Wolfgang: did we do this to capture small local variations within cells better?

I wouldn't think so. I've done some software archeology and we used the +2 
both for the temperature and the composition before that was unified into the 
current function -- in fact, one can trace this back to step-31 when we only 
had temperature :-)

The reasoning may have been that we have to assemble a term of the form
   u . grad phi_i * phi_j
with a total polynomial degree of
   stokes_degree + 2 * temp_degree - 1
which would suggest a Gauss formula of degree
   temp_degree + stokes_degree/2
rounded up if necessary. Does this sound reasonable? It would boil down to
   temp_degree + 1
in the most common case.

Best
  Wolfgang
-- 
------------------------------------------------------------------------
Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/