David's right....

On Sep 27, 2008, at 11:26 AM, David Knezevic wrote:

> Well, the problem I think is that the gradients are not well-defined  
> at
> node points, since finite element solutions are piecewise polynomials.

Yep.. for your normal Lagrange elements the gradient is undefined on  
the element boundaries (including the nodes).  Now, for C1 continuous  
elements (such as Clough-Toucher's, Hermite's, etc.) you should be  
able to get the value of the gradient at the nodes pretty easily: it  
should be in your solution vector.  Obviously, I've never used these  
elements or I would know the answer to that... maybe Roy could fill us  
in.

> One way to get an answer (John suggested this to me once) is to  
> compute
> the gradients at quadrature points and then do an L2 projection of  
> that
> solution, and then just sample the projected solution at the nodes.

Yep... this is what's calle "Gradient Recovery".  There are several  
methods for doing this...

Derek

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