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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