Finite Element Galerkin Models and Identified Finite Element Models-A Comparative Study

A new approach to derive a finite element discretisation of PDE equations soley from pointwise observations is compared, in terms of approximation accuracy, with the standard finite element Galerkin approach which assumes knowledge of the governing PDE's. It is shown both in theory and by means of an example that, for a given model order, the identified model is more accurate than the equivalent finite element Galerkin approximation derived from the original PDE's.