ABSTRACT
This chapter describes a variety of recent results concerning superconvergence and extrapolation for the finite element method for second order elliptic problems. The results are based on some new local pointwise estimates. The chapter discusses the local pointwise error estimates which are valid for a large variety of finite element spaces on irregular quasi-uniform grids. It presents some consequences of these estimates which are weak error expansions in the form of inequalities. The chapter contains some consequences of these error expansion inequalities. In particular, conditions are given under which the error on an element is dominated by the interpolation error on that element. The chapter contains a new approach to Richardson extrapolation and contains some new superconvergence results. In Hoffmann, Schatz and Wittum a local a posteriori error estimator will be analyzed for some smooth problems and model corner problems in the plane.
