FInite Element Method overview

Since FEM is well documented and quite popular I will start to build my work around it.

The FEM can be used to calculate the field inside a space.

but first you need to define:

1. the boundary conditions which will helps to resolve the unknown element of the differential solution.
2. the mesh structure (or sometimes called triangulation) of studied surface or volume.(Series of triangle for 2D meshing or series of tetrahehra or pyranids for 3D meshing)
   

Once the mesh and the boundary conditions are defined you can solve the partial differential equation(PDE) using Finite Element Method (FEM) in order calculate the fields of the studied surface or volume.

To program it you will need to find a proper way to create the mesh...
freeFEM++ or getFEM libs can do most of the work for you, but first we need to understand how they program is working....