Nic Fillion recently presented at the Workshop on Modelling and Reasoning in the Sciences at Yang Ming University, in Taiwan. The workshop was organized by Professor Karen Yan and took place on November 24 and 25. It gathered scholars specializing in history and philosophy of science from six countries.
Nic's talk, entitled "Concepts of Approximate Solutions and the Finite Element Method: A Philosophical Take on Variational Crimes" discussed a computational method that is very widely used in applied mathematics and engineering. Despite its stunning success in applications, this method nevertheless violates some traditional standards used to characterize good approximations in scientific modelling. The talk articulates two different perspectives on approximation, and explained how only one explains the success of finite element methods.