[dune-pdelab] Evaluate solution through a native DOF vector

[Carsten Gräser]

Hi,
I'm not a PDELab expert, but ...

Am 25.11.2016 um 12:52 schrieb Lukas Riedel:
>> you can simply evaluate the shapefunctions at the point of your delta
>> functions. There is no need to use numerical integration.
> 
> Perfect. I’ll try that.
... the proposed solution sounds very dangerous to me.
Once your measurement is not a volume integral you cannot
localize without taking special care.

In case of a point evaluation at p you will run into trouble
if p is not in the interior of an element. Then the result of
the proposed procedure will not be u(p) but k_p*u(p) where k_p
is the number of elements that contain p.

In this case you could e.g. set a flag once you first
found p in an element and do no evaluation afterwards.
Or you can count the number of elements containing p
and divide by this afterwards. The latter will give you
some kind of averaging in case of discontinuous solutions.

Best,
Carsten



> 
>>> On a side note, I achieved what I originally wanted by taking the first element of the MultiIndex I receive from the containerIndex() function. This works because my GFS is scalar.
>>
>> a) it will not work anymore, when you use other measurment functions
>> b) searching the pos is quite expensive. you might use the hierarchic
>>   search, but still it might be expensive.
> 
> I have few measurement positions and I only need to assemble this ‘measurement operator’ once for every position. So the expensive search is not a large concern.
> 
> Cheers,
> Lukas

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