Re: [Libmesh-users] Getting access to gradients at node points From: Nasser Mohieddin Abukhdeir - 2008-09-27 18:24:58 ```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: http://www3.interscience.wiley.com/journal/110544657/abstract Nasser Mohieddin Abukhdeir Graduate Student (Materials Modeling Research Group) McGill University - Department of Chemical Engineering http://webpages.mcgill.ca/students/nabukh/web/ http://mmrg.chemeng.mcgill.ca/ 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 >> 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 > ```