I found a few references on gradient recovery, seems a bit expensive to
do concurrently in my simulations (both directly or through some
Galerkin method), so I'll just do it a posteriori as a separate FEM
run. I found a decent paper describing direct and Galerkin methods.
Switching to Hermite or any higher order elements is simply too
expensive for my problems, at least with these gradient recovery methods
I can delay the work until after the main computation is complete.
BTW, here is a paper that I found useful in understanding these methods:
Nasser Mohieddin Abukhdeir
Graduate Student (Materials Modeling Research Group)
McGill University - Department of Chemical Engineering
Derek Gaston wrote:
> 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
>> 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
>> One way to get an answer (John suggested this to me once) is to
>> the gradients at quadrature points and then do an L2 projection of
>> 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...