# Finite Element Method (FEM) and partial differential equation methods

Finite Element Analysis is widely used in Computer Aided Engineering (CAE). It might be used to verify an engineering design, for example the crash worthiness of a car, or the safety of a large mechanical engineering project.

The finite element method is a method to approximate the solutions of partial differential equations with boundary conditions. It can therefore only be used where the physical properties can be expressed in terms of partial differential equations. (see differential equations)

This is a numerical method. It is a very powerful method but it is very computationally intensive, at the moment I'm not sure if it could be used for real-time simulation of mechanical systems?

I don't claim to fully understand the method, as far as I can work out it involves the following stages:

1. Express the problem in terms of partial differential equations, conservation laws such as conservation of mass, energy or momentum can be expressed in these terms.
2. Somehow the shape needs to be defined (is this what is meant by the boundary conditions?)
3. This is solved numerically.
4. The results are displayed, this may involve grid / mesh generation software.
##### Boundary Element Method

The Boundary Element Method (BEM, also referred to as Boundary Integral Equation or BIE) uses elements along the boundary of the model,
rather than throughout the model.

In the BEM discretization takes place on the boundary.

In the FEM discretization takes place on the domains.

##### Computation Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is the numerical analysis of fluid flows. This can be done via various techniques, including FEM..

##### Discrete Element Method

The Discrete Element Method (DEM) is used in cases where the model is composed of particulate matter (e.g. soils) rather than a continuum.

##### Finite Difference Time Domain Pages

The Finite Difference Time Domain method (FDTD) is typically used for electromagnetic analysis. The following pages have information on this
topic.

FTDT BibTeX File This is a bibliography of FDTD work

##### Finite Volume Method

A toolkit for multi-physics computational continuum mechanics modeling based on three dimensional unstructured meshes using finite
volume / finite element techniques.