The finite element method (FEM) is a numerical technique for solving problems in engineering and scientific disciplines that are described by partial differential equations (PDEs). The FEM is a powerful tool that can be used to approximate complex solutions to PDEs. In the FEM, the domain of the PDE is divided into small elements, and the solution to the PDE is approximated using a set of basis functions defined on each element. The coefficients of the basis functions are determined by solving a system of linear equations. The FEM can be used to solve problems in a wide variety of fields, including mechanics, electromagnetics, heat transfer, acoustics, and fluid dynamics.
The finite element method was first developed in the 1940s by mathematicians who were working on aircraft design. Since then, it has been extensively used in many different fields. One of the advantages of the FEM is that it can be used to solve problems that cannot be solved using traditional methods such as calculus or differential equations. Another advantage is that the FEM can be used to obtain accurate solutions to PDEs without having to discretize the domain into small elements. This allows for more flexibility in how the problem is solved.
There are many different software packages available that allow for easy implementation of the FEM. These software packages make it possible for engineers and scientists to solve complex problems without having to write their own code or derive their own algorithms.