The finite element method is a method for solving partial differential equations (PDEs). For example a PDE will involve a function u(x) defined for all x in the domain with respect to some given boundary condition. The purpose of the method is to determine an approximation to the function u(x).
The method requires the discretisation of the domain into subregions or cells. For example a two-dimensional domain can be divided and approximated by a set of triangles (the cells). On each cell the function is approximated by a characteristic form. For example u(x) can be approximated by a linear function on each triangle.