In Encore at Sandia you get the choice to either compute L_Inf at the
quadrature points or at the nodes.
There really isn't a good way to give L_Inf for a finite element
calculation.... because our solutions are continuous functions. The
finite difference guys would just take the difference at all the nodes
and find the largest one.... but that doesn't quite work for us
(especially with higher order elements).
Personally, I prefer finding the L_Inf error at quadrature points...
one nice thing about this is that if you want a better calculation of
your error... you just up your number of quadrature points. This is
essentially the same thing as comparing to a non-polynomial exact
solution (one you can't integrate exactly).... you do _something_ that
will give you a good answer... but if you want a better answer you
crank up the quadrature rule.
Derek
On Aug 26, 2008, at 8:10 AM, John Peterson wrote:
> On Tue, Aug 26, 2008 at 5:02 AM, Tim Kroeger
> <[EMAIL PROTECTED]> wrote:
>> Dear John,
>>
>> On Mon, 25 Aug 2008, John Peterson wrote:
>>
>>> On Mon, Aug 25, 2008 at 8:28 AM, Tim Kroeger
>>
>>>> Would you please be so kind and check that changes in (provided
>>>> you like
>>>> them)?
>>>
>>> I'll take a look at this patch today. Thanks!
>>
>> So, what was the result of looking at the patch?
>
> 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? I
> don't know of an efficient, simple algorithm for estimating L-infty
> error ... perhaps there is something out there?
>
> My preference would be to leave out the L_INF calculation rather than
> return a potentially wrong value, but I would like the other
> developers (esp. Roy, who is on holiday now) to comment as well.
>
> --
> John
>
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