Abstract
The finite element method is used to find solution of a complicated problem by replacing it by a simpler one. In finding the solution, the actual problem is replaced by a simpler one; therefore,, one is able to find only an approximate solution rather than the exact solution. In the finite element method, it is possible to improve or refine the approximate solution by spending more computational effort. This method considers the solution region as built up of many small, interconnected subregions called finite elements. In each piece or element, a convenient approximate solution is assumed and the conditions of overall equilibrium of the structure are derived. The satisfaction of these conditions yields an approximate solution for the displacements and stresses. Although the method has been extensively used in the field of structural mechanics, it has been successfully applied to solve several other types of engineering problems, such as heat conduction, fluid dynamics, seepage flow, and electric and magnetic fields. These applications prompted mathematicians to use this technique for the solution of complicated boundary value and other problems.
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