FEM data interpolation
Hi all,
I need some good interpolation techniques for interpolation of FEM data from cell center of linear triangle to the triangle nodes. I tried to search the net but these days you get more junk on the web than useful information...and i don't really have the to sort the junk information. If anybody out there knows please direct me to appropriate source. I tried inversedistance weighting and cell area/volume averaging but they are not satisfactory. thanks abhijit 
Re: FEM data interpolation
Since no one has replied to your request, let me give you a suggestion. It is what I would try first. Suppose your trianglecentered data were averages of unknown values at the corners of the triangles, i.e. for some triangle, (val_1 + val_2 + val_3)/3 = val_center. You have one equation like this for every triangle. This gives a set of algebraic equations to be solved for the data at the corner nodes. BUT, you have more unknowns than equations. Suplement these equations with boundary conditions to try to get a complete set of equations which can be solved in the usual way. If your best efforts do not produce a complete set of equations, then look for a method such as singular value decomposition (SVD). There are standard routines for doing this. One reference is the series "Numerical Methods in C/Fortran/C++...".
Remember though, such inverse problems are often unstable. Data has been lost in the averaging process which may not be recoverable. 
Re: FEM data interpolation
You should search cells which share the node. Then, volume (surface) weighted average is enough. Ie, Q_node = sum(V_cell*Q_center)/sum(V_cell)

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