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I mean in which industry it is being widely used. Is it aviation or automobile or mechanical, etc..,
It is used in each and every industry where the new technology or process for developing a new product, is being developed and it is required whether such process or the product will be able to sustain the application loads at the user end and for how long.
FEA can help to understand the limits to which a particular part has to be subjected to and for how long the performance can be expected.
Because finite element method can deal more accurate than finite difference and boundary element methods with complicated gdomain geometry and complicated boundary and initial conditions in addition to deal with multi phase problems like fluid -structure interaction better than other numerical techniques
Finite Element Analysis is most extensively used in the analysis of machines in Automobile, Production industries etc. In construction also it is being used. Recently I did strutural analysis using Nastran and come up with expected results.