Postprocessing of a finite element scheme with linear elements

In this contribution we first give a brief survey of postprocessing techniques for accelerating the convergence of finite element schemes for elliptic problems. We also generalize a local superconvergence technique recently analyzed by Křížek and Neittaanmäki to a global technique. Finally, we show that it is possible to obtain O(h4) accuracy for the gradient in some cases when only linear elements are used. Numerical tests are presented.peerReviewe