The Finite element method (FEM) , Or finite element analysis (FEA),is based on the idea of building a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces.Since the actual problem is replaced with a simple one in finding the solution , we will able to find an approximate solution than the exact solution.The existing mathematical tools will not be sufficient to find the exact solution for most of the practical problems.
Thus in the absence of any other convenient method to find even the approximate solution of a given problem , we have to prefer the finite element method.Using this method , it is even possible to improve or refine the approximate solution by using computers of higher processing capabilities.