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The finite element method (FEM)
Sometimes referred to as finite element analysis (FEA) , it is a numerical technique for finding approximate solutions of partial differential equations (PDE) and integral equations. standard techniques such as Euler's method, Runge-Kutta are invloved in rendering the PDE into an approximating system of ordinary differential equations and then numerically initegrating. eliminating the differential equation completely is done for steady state problem. the main challenge in solvong PDE i is to create an equation that approximates the equation to be studied, but is numerically stable,(ie ,errors in the input data and intermediate calculations do not accumulate and cause the resulting output to be meaningless.) The Finite Element Method is a good choice for solving partial differential equations over complicated domains such as cars and oil pipelines.

Applications of FEM:
Mechanical related industries like aeronautical, biomechanical, and automotive industries commonly use integrated FEM in design and development of their products. thermal, electromagnetic, fluid, and structural working environment are included in the modern FEM packages. It allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements. Wide simulation options for controlling the complexity of both modeling and analysis of a system is provided by the FEM software, FEM allows entire designs to be constructed, refined, and optimized before the design is manufactured.standard of engineering designs and the methodology of the design process in many industrial applications has been advanced due to this vert useful tool.

For more visit:
http://en.wikipediawiki/Finite_element_method
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