Because that is the name of the technique used to solve the underlying mathematics.
It was invented by Professor Richard Courant in 1943, but did not become popular until the advent of powerful mainframe computers in the 1960's. Since then, the capabilities of the technique have grown explosively.
Serious finite element analysis has been possible on PCs for at least the last decade. As the price of hardware comes down, the range of economically feasible projects we can undertake increases.
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What Is Finite Element Analysis: Why is it Called Finite Element Analysis? 
