[Nek5000-users] Computing higher order derivatives

[nek5000-users at lists.mcs.anl.gov]

Hi Praveen,

To compute continuous weak approximations to du/dy (say), you
would do the following:

       call gradm1(ux,uy,uz,u)

       n = nx1*ny1*nz1*nelv
       call col2  (uy,bm1,n)
       call dssum (uy,nx1,ny1,nz1)
       call col2  (uy,binvm1,n)

assuming all arrays appropriately declared.

Paul


On Wed, 15 Jan 2014, nek5000-users at lists.mcs.anl.gov wrote:

>
> Hi Praveen,
>
> Correct, the functions are only C^0 continuous.  However,
> if the solution is C-infinity, the SEM will
> converge exponentially fast to the continuous solution.
>
> When taking such high-order derivatives, it's a good idea
> to be working in the full precision of the solution --- are
> you postprocessing when you apply chebfun?  If so, make certain
> that your nek output data has full 64-bit precision (typ. 15 digits).
>
> Another approach you could try would be to perform, say, a
> least squares fit or other type of projection onto a C-infinity
> basis (e.g., Fourier, iff your function is periodic) and then
> differentiate that.
>
> Paul
>
>
> On Wed, 15 Jan 2014, nek5000-users at lists.mcs.anl.gov wrote:
>
>> Hello
>> For doing stability analysis I need upto third derivatives of velocity. Is
>> this already available in nek ? I tried to compute derivatives of the nek
>> solution using chebfun but the second and higher derivatives are coming out
>> to be discontinuous ? This is expected I suppose, since the solution is
>> only C^0. Can I repeatedly use gradm1 to get higher derivatives ? Does
>> gradm1 do some projection ?
>> 
>> Thanks
>> praveen
>> 
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