A Note on a Priori L-error Estimates for the Obstacle Problem

This paper is concerned with a priori error estimates for the piecewise linear nite element approximation of the classical obstacle problem. We demonstrate by means of two onedimensional counterexamples that the L2-error between the exact solution u and the nite element approximation uh is typically not of order two even if the exact solution is in H 2(Ω) and an estimate of the form ‖u − uh‖H1 ≤ Ch holds true. This shows that the classical Aubin-Nitsche trick which yields a doubling of the order of convergence when passing over from the H1to the L2-norm cannot be generalized to the obstacle problem.