Title: Can a finite element method perform arbitrarily badly?
Abstract: The talk will simply go through the paper of the same title given by Ivo Babushka and John Osborn, 1999. In that paper, they construct a toy
elliptic boundary value problem which converges arbitrary slowly in
almost all reasonable norms. Moreover, adaptive procedures cannot save
the convergence rate. The problem is 1D with piecewise polynomial
elements, and the rest is just elementary arithmetic. But revisit such
an easy case may suggest a different view of classical methods.