Can a finite element method perform arbitrarily badly?

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy nor m, and show that adaptive procedures cannot improve this slow convergence. We also show that the L-2-norm and the nodal point errors converge arbitrar ily slowly. With the L-2-norm two cases need to be distinguished, and the u sual duality principle does not characterize the error completely. The cons tructed elliptic problems are one dimensional.