On Tue, Aug 26, 2008 at 9:20 AM, Tim Kroeger
<[EMAIL PROTECTED]> wrote:
> Dear John,
>
> 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.
> 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.
--
John
-------------------------------------------------------------------------
This SF.Net email is sponsored by the Moblin Your Move Developer's challenge
Build the coolest Linux based applications with Moblin SDK & win great prizes
Grand prize is a trip for two to an Open Source event anywhere in the world
http://moblin-contest.org/redirect.php?banner_id=100&url=/
_______________________________________________
Libmesh-users mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/libmesh-users
