FEM

- A numerical method
- Mathematical representation of an actual problem
- Approximate method


The Finite Element Method only makes calculations at a limited (Finite) number of points and then interpolates the results for the entire domain (surface or volume).
Finite – Any continuous object has infinite degrees of freedom and it is not possible to solve the
problem in this format. The Finite Element Method reduces the degrees of freedom from infinite to finite with the help of discretization or meshing (nodes and elements).

Element 

 All of the calculations are made at a limited number of points known as nodes. The entity joining nodes and forming a specific shape such as quadrilateral or triangular is known as an Element. To get the value of a variable (say displacement) anywhere in between the calculation points, an interpolation function (as per the shape of the element) is used.

Method - There are 3 methods to solve any engineering problem. Finite element analysis belongs to numerical method category.