Explain me the Finite Elemente Method

The finite element method ( FE M ) is a numerical method used to solve partial differential equations ( P DE s ) by approxim ating the solution using a finite number of elements . It is a powerful tool for solving a wide range of problems in engineering , physics , and other fields . \n \n The basic idea behind F EM is to divide the domain of interest into a large number of small , non - over l apping elements , such as tri angles or rect angles . Each element is assigned a set of basis functions , which are used to approximate the solution within the element . The solution is then constructed by combining the solutions of the individual elements using a technique called inter polation . \n \n One of the key advantages of F EM is its ability to handle complex ge omet ries and boundary conditions . It can also be used to solve problems with varying degrees of smooth ness , such as those involving partial deriv atives . Additionally , F EM can be used to solve problems with non linear ities and time - dependent behavior . \n \n FE M is widely used in a variety of applications , including structural analysis , fluid dynamics , heat transfer , and elect romag net ism . It is also used in the design of engineering systems , such as br idges , buildings , and aircraft . \n \n Over all , F EM is a powerful and vers atile tool for solving complex problems in engineering and physics . It is widely used and continues to be an active area of research and development . </s>