On Tue, Aug 26, 2008 at 10:22 AM, Tim Kroeger
<[EMAIL PROTECTED]> wrote:
> 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).
Unfortunately the error is not a linear function in general, even
though the approximate solution may be.
--
John
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