Review on finite element method

Abstract

In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and its future. The eventual intension of using FEM is to determine the nodal solution of a particular problem under study. The power of FEM is its ability to discretize complex problems and analyse it part by part. Irrespective of the geometry of the problem, with proper mesh refinement, FEM provides very accurate solution. Therefore, FEM is a technique in which a given domain is represented as a collection of simple domains, called finite elements, so that it is possible to systematically construct the approximation functions needed in a variational or weighted-residual approximation of the solution of a problem over each element.

Keywords: Weak Formulation, Discretisation, Numerical methods, Finite element method, Global equations, Nodal solution