Topic: The finite element method(FEM) simulation
The finite element method (FEM) is a numerical technique for finding approximate solutions to equilibrium or boundary value
problems, eigenvalue problems, propagation or initial value problems for partial differential equations. Difference of FEM with other numerical methodology (especially Finite differential method, FDM) is subdividing a domain into elements. Element can become any shape and size. So it is possible to fill boundary with elements in spite of strange shape of boundary.
This process needs mesh generation. There are many open source mesh generator and they operates like this image.Generally, triangle (2D) or tetrahedron (3D) shape is used for subdividing domain.
FEM is nowadays widely used by these properties. And finite element method include variational formulation. Galerkin method is widely used out of the others because it is most common.
(ref. wikipedia 'fem')