Spectral Element Method

[Robert Edmonds]

Shot in the dark here on storm track, but what the heck. If anyone knows anything about spectral element methods I would be interested in learning from your post. I have been thinking I need try something besides finite differencing with a (personal) model I've been developing, and I believe this method may hold the solution for me. So far most of what I have read has left me lost and confused.

 

[David Wolfson]

I wasn't going to venture anywhere near this thread because there're many far more technically proficient here. But I think Robert is looking for some feedback and I'll throw in something that's hopefully value-added and others may want to chip in.

What particular applications you're interested in play a big part. My impression from other threads is your particular interest involves doppler data processing to deduce upper wind fields, curl, div, and such. When I read this question Kalman filtering immediately popped into mind as an alternative to finite differencing.

Except in the middle of thunderstorms the horizontal velocities are much greater than the vertical velocities. And the horizontal velocities only change (i.e. non-linear influences) rather slowly in response to rather well-known principles like Navier-Stokes , which are of larger scale at levels above the surface.

Kalman filtering is a category of numerical method that uses inference about state T+1 against actual T+1 to refine the inference in the presence of Gaussian noise. It's I think used in radar tracking applications and may be something worth looking into. FWIW.