[Nek5000-users] Computing higher order derivatives

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

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
>