The Derivative Patch Interpolating Recovery Technique for Finite Element Approximations

Abstract

A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case. It is shown that the convergence rate of the recovered gradient admits superconvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultraconvergence) at an internal node point when even order finite element spaces and local uniform meshes are used.