FEM Shape Function Derivation
 

Is it possible to derive FEM shape function for arbitrary polyhedral mesh?

Re: FEM Shape Function Derivation
 

See the book by Eugene Wachspress, "A Rational Finite Element Basis," Academic Press 1975.

I think one reason this approach never caught on is because of the difficulty of integrating over polyhedrons with more than four sides. Also, parametric mappings have proved to be more versatile. I found Wachspress' work useful in understanding why some quad mappings behave so poorly.