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I wish to create a FEM mesh to solve an inverse elasticity problem, for an irregular domain. This domain is given by a medical image, so it is discretised and each square on the grid has one scalar value.

I assume the discretized and band-limited nature of the domain can inform my choice of FEM mesh, but have not seen this particular case discussed in my source books.

Consider the 1D case. I know from Lagrange that for a set of regular samples of length n I can construct a polynomial of order n−1. This is one way of expressing the bandwith and information limitations of the image.

My gut tells me that for this reason, I can mesh with squares at the same resolution as the image, using linear shape functions, and capture all the information available in the image. But I lack the math chops to derive this result. Is it correct?

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    $\begingroup$ You might be better served by treating the pixels of the image as the nodes of an interpolating quadrilateral mesh rather than as the cell centers. $\endgroup$
    – Bill Barth
    Commented Feb 25, 2015 at 15:55
  • $\begingroup$ You can try to reconstruct the geometry based on image processing. $\endgroup$
    – nicoguaro
    Commented Feb 25, 2015 at 20:29
  • $\begingroup$ This is an exciting question on which more research is needed. $\endgroup$ Commented Jan 15, 2017 at 20:42

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