Numerical evaluation of F.E.M. with application to the 1-D advection-diffusion problem.

In this paper we present a numerical procedure to evaluate the efficiency of finite element numerical methods. We improve some of the ideas proposed in previous works, and we give a partly theoretical partly empirical justification in a general framework. The proposed procedure performs an eigenvalue computation, and requires the knowledge of the behavior of the exact operator in order to choose proper norms for the evaluations. In the experiments we focus our attention on the 1-D advection-diffusion problem: we show that our numerical procedure gives actually very sharp indications about the optimality of the tested numerical methods.