[Nek5000-users] Computing higher order derivatives

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

On Wed, Jan 15, 2014 at 4:52 PM, <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
>

Hi Paul

My problem is flow in a channel and I want to study some stability of 1-d
velocity profile.

In usrchk, I write the GLL nodes and solutions to a file with some 14-15
decimal places.

In matlab I construct a piecwise barycentric lagrange formula. This is used
by chebfun which automatically constructs a piecewise chebyshev
approximation. It exactly and automatically recognizes the element
boundaries !!! chebfun can also construct a single chebyshev approximation
but needs ~65000 nodes and the higher derivatives have large error at the
end points.

Is it possible to find weak derivatives inside nek, e.g, find g such that

int(g * phi) = int(du/dy * phi) for all phi

Then g will give a continuous approximation to du/dy.

Thanks
praveen
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