Student: You said all numerical techniques are based on the same philosophy that is to convert the continuous nature of the DE into algebraic simultaneous equation. So what makes FE an FE, in other words, what differentiates FE from the rest of the numerical techniques?
Dr Airil: What makes FE and FE, in other words, what differentiates FE from the rest of the numerical techniques is the use of predefined shape functions.
Student: That's it?
Dr Airil: Yes, that is about it.
Student: What about the use of degree of freedom or dof?
Dr Airil: The use of dof in FE is a standard math terms actually, it is equivalent to nodal values as in Finite Difference and other techniques. In fact the words dof and nodal values are themselves interchangeable.
Student: What about Galerkin (or weighted residual method, WRM) formulation, is not it characterizes FE?
Dr Airil: Yes but not uniquely, many other numerical techniques employ Galerkin (or WRM for that matter) like Boundary Element Method or BEM and Meshfree (or Meshless) method. In fact, FEM itself can be derived from various sources like principle of virtual works and minimum potential energy.
Student: So, it is the use of predefined shape functions that differentiates FE from the rest of the numerical techniques. This what makes FE an FE.