Some gradient superconvergence results in the finite element method

Abstract

This paper is concerned with the phenomenon of gradient superconvergence of finite element approximations to the solutions of two-dimensional second order elliptic boundary value problems. The original concept of gradient superconvergence is that there exist certain points in each element at which the gradient of the finite element approximation has a higher rate of convergence to the gradient of the true solution in a discrete analogue of a Lebesgue norm than that found globally in the Lebesgue norm itself.