> Applying FEM to real-life problems can involve the resolving of quite a lot of "little" practical and theoretical gotchas, bugs, etc. FEM at it's core ends u

> Applying FEM to real-life problems can involve the resolving of quite a lot of "little" practical and theoretical gotchas, bugs, etc. FEM at it's core ends up being just a technique to find approximate solutions to problems expressed with partial differential equations. Finding solutions to practical problems that meet both boundary conditions and domain is practically impossible to have with analytical methods. FEM trades off correctness with an approximation that can be exact in prescribed boundary conditions but is an approximation in both how domains are expressed and the solution,and has nice properties such as the approximation errors converging to the exact solution by refining the approximation. This means exponentially larger computational budgets.