# Explain finite element method of simulation with suitable example .My posted question is related with Research Methodology subject .

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Finite element analysis (FEA) is essentially exactly what it sounds like. You break down the differential equation or integral into finite elements over its boundary in order to approximate a solution. Think of it like approximating the area under an inverted parabola and x-axis by summing the area of rectangles divided over the span between the two x-intercepts. The smaller the width of each rectangle, the more accurate of an approximation you will have of the area. That is essentially the method; however, one of the fundamental uses of FEA is that the finite elements do not need to be evenly ditributed. That is why this method of simulation is most often used when the desired degree of percision isn't the same over the entire domain.

For instance, Aerospace Engineers could use FEA to do boundary layer analysis of flow over an airfoil because you would want the solution to be the most percise at the leading and trailing edges. FEA can save a lot of computation time by having a lower degree of percision in areas you don't necessairly care about, and concentrating that extra computation power in the areas you do want a good deal of percision in. The same could be said about calculating the bending stress in a beam. You would concentrate the highest degree of percision at the bending point in the beam, and lessen the degree of percision as you move farther away from the bending point.