For example, the basic concept of finite element analysis (FEA) is to replace complex problems with simpler ones before solving them. It regards the solution domain as composed of many interrelated subdomains called finite element, assumes a suitable (relatively simple) approximate solution for each element, and then deduces the general satisfaction conditions (such as structural equilibrium conditions) for solving this domain, thus obtaining the solution of the problem. This solution is not an exact solution, but an approximate solution, because the actual problem is replaced by a simpler one. Because most practical problems are difficult to get exact solutions, the finite element method is not only accurate, but also can adapt to various complex shapes, so it has become an effective means of engineering analysis.

Finite element is a discrete element that can represent an actual continuous domain together. The concept of finite element has been produced and applied centuries ago, such as using polygons (finite linear elements) to approximate a circle to find its circumference, but it was only recently put forward as a method. The finite element method, originally called matrix approximation method, is applied to the structural strength calculation of aircraft, which has aroused great interest of scientists engaged in mechanical research because of its convenience, practicality and effectiveness. After decades of efforts, with the rapid development and popularization of computer technology, the finite element method has rapidly expanded from structural engineering strength analysis and calculation to almost all scientific and technological fields, and has become a colorful, widely used, practical and efficient numerical analysis method.