This MIT professor looks like a very intelligent guy, and I agree with what he says, but the article shows that the reporter did not understand some things.
Plasticity theory is presented as an alternative to the finite element method, but in fact they are usually used together. While plasticity theory explains how materials deform, the FE method makes possible to apply this theory to complex structures.
In any case, the problem cannot be FEM, but how it is applied and how the results are interpreted. It is very likely (even expected) that applying the requirements used for steel or concrete structures to the Pantheon will give you wrong results, but that does not mean FEM is the problem. Blindly doing simulations without having a good model and being very careful of how boundary conditions are applied and how to interpret the results, on the other hand, is becoming a greater problem as the necessary hardware becomes more affordable.
Plasticity theory is presented as an alternative to the finite element method, but in fact they are usually used together. While plasticity theory explains how materials deform, the FE method makes possible to apply this theory to complex structures.
In any case, the problem cannot be FEM, but how it is applied and how the results are interpreted. It is very likely (even expected) that applying the requirements used for steel or concrete structures to the Pantheon will give you wrong results, but that does not mean FEM is the problem. Blindly doing simulations without having a good model and being very careful of how boundary conditions are applied and how to interpret the results, on the other hand, is becoming a greater problem as the necessary hardware becomes more affordable.