[Nek5000-users] A good way to approximate second derivatives?

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

Hello!

This is the first time I write to this list.
I am a PhD student at KTH Mechanics, and use Nek5000 mostly to get  
steady solutions for my linear stability calculations (where the  
steadiness is imposed geometrically, by boundary conditions) on 2D  
wakes and jets. The stability calculation is performed on a different  
grid, in another code.

I wrote a script where I interpolate the solution form Nek5000 exactly  
to my stability grid using the Legendre basis functions, and for the  
flow variables (U,V,P) and their first derivatives this works fine.  
However, now I am using the same steady solution to calculate  
stability with surface tension (since for slowly developing flows the  
steady state without surface tension can still be used). In this new  
setting, the second derivatives (Uxx,Uyy,Vxx,Vyy) are also needed.

Therefore I wonder if there is any standard way to approximate the  
second derivatives of the flow variables in Nek5000?
The basis functions are only C1-continuous across the element  
boundaries, and even if they would have been continuous, the second  
derivatives are always noisy, e.g. if taken from experimental data.
Currently I use finite differences combined with a smooth function in  
Matlab with a 5-point moving average.

Thank you for input or better ideas,

Outi Tammisola