From my experience in the field, convergence studies are something everyone knows they should do, but never actually happen because results are always needed ye

From my experience in the field, convergence studies are something everyone knows they should do, but never actually happen because results are always needed yesterday. As for automating it, sure for a model like that with tens or hundreds of elements, it would take seconds on a modern computer, great. Except, model complexity always scales to reach the boundary of reasonable computation time on modern computers. This has to be a corollary to Moore's law or something. Recently I've been working on a model with tens of millions of elements. Takes 12-ish hours to solve a few load cases. A good convergence study might take weeks. Thankfully, finite element solvers have gotten much better at tolerating bad element geometry, and at warning users for about geometry likely resulting in bad results. Plus things like NASTRAN's integrated extrapolation of stresses at element corners, instead of outputting only element stresses and having the analyst extrapolate. A colleague of mine ran some tests a few years ago at a customer's request, running a very coarse model with corner stress extrapolation enabled. Results were plenty good, well within normal engineering uncertainties and tolerances. FEM was still pretty young in the early 90s and probably required very experienced/knowledgeable engineers to use it. As with most things, it's gotten more and more user frendly, and more and more software are taking very automated and behind the scenes approaches to FE (ANSYS Workbench, Solidworks Simulations, Simlab, etc). It has its good and bad sides.