ABSTRACT
We present a method for obtaining superconvergent approximations of linear functionals. We present an illustration of this idea in the framework of convection-diffusion equations. We use the approximation given by the discontinuous Galerkin method with polynomials of degree k. Instead of the classical order of convergence of 2k, we prove that we can obtain an approximation of order 4k. Numerical results that confirm this theoretical finding are presented.