FEA vs. FEM

Today when we hear about finite element method (FEM), the first thing that comes across our mind would be a beautiful picture like this:

Simulation result adapted from DTE Desktop Engineering

which is not entirely true.

It has been mentioned here that continuum mechanics is essentially solving for solutions of partial differential equations (PDEs) that defines a material body. In mathematics, PDEs can be solved either analytically or numerically. Analytical methods are those that we have all heard of from our mathematics course (but do not worry if you haven't yet!!), these include:

• separation of variables,
• change of variables,
• method of characteristics,
• to name but a few...

Similarly in mathematics, there are three widely used methods for solving PDEs numerically. These are the:

• finite difference method,
• finite volume method, and
• finite element method.

The most well-known practical application of FEM (that is to solve PDEs in continuum mechanics problems) is often known as the finite element analysis (FEA), which usually involves software capable of doing pre-processing, perform analysis using FEM and generating results (post-processing).

In conclusion, FEM is a method one uses for performing an engineering analysis called FEA.