Dear John,
On Tue, 26 Aug 2008, John Peterson wrote:
> On Tue, Aug 26, 2008 at 9:20 AM, Tim Kroeger
>>
>> On Tue, 26 Aug 2008, John Peterson wrote:
>>
>>> I'm not sure about your implementation of L_INF. You're taking
>>>
>>> ||e||_{\infty} = max_q |e(x_q)|
>>>
>>> where x_q are the quadrature points. In fact, isn't the solution
>>> sometimes superconvergent at the quadrature points, and therefore this
>>> approximation could drastically under-predict the L-infty norm?
>>
>> Oh, I see, I (again) forgot that people are using different ansatz functions
>> than piecewise linear (for which this is obviously correct).
>
> Sorry, I'm a little slow. The formula above is correct for piecewise
> linears? I can see this for linear elements in 1D, with a 1-point
> quadrature rule. But this implies it's not true for a 2-point
> rule... etc.
Oops, I'm very sorry. I mixed up quadrature points and nodes. What I
meant was that for a linear function on a tetrahedron, its maximal
value can be obtained by evaluating it at the corners of
the tetrahedron only (and taking the max of these values).
>> What about returning this value as the DISCRETE_L_INF norm instead? In
>> particular since the FEMNormType enum offers this norm anyway.
>
> I think this might be confusing ... the DISCRETE_ versions are meant
> to be for R^n vectors, and in this case of course you can get the
> "exact" L_INF. I'd prefer adding a new enum called APPROXIMATE_L_INF
> (or something similar). The user would know immediately that he was
> getting an approximation to the true L-infty norm, and in the
> documentation we could mention (as Derek said) that one can improve
> the approximation by increasing the number of quadrature points.
Yes, I agree with that.
Also, there is a different error in my patch: In parallel, I sum up
the L-infty norms of all the processors, instead of taking their max
value.
I will send you a corrected patch tomorrow.
Sorry again.
Best Regards,
Tim
--
Dr. Tim Kroeger Phone +49-421-218-7710
[EMAIL PROTECTED], [EMAIL PROTECTED] Fax +49-421-218-4236
MeVis Research GmbH, Universitaetsallee 29, 28359 Bremen, Germany
Amtsgericht Bremen HRB 16222
Geschaeftsfuehrer: Prof. Dr. H.-O. Peitgen
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