SUPERCONVERGENCE OF TETRAHEDRAL QUADRATIC FINITE ELEMENTS

For a model elliptic boundary value problem we will prove that on strongly regularfamilies of uniform tetrahedral partitions of a pohyhedral domain,the gradient of thequadratic finite element approximation is superclose to the gradient of the quadratic La-grange interpolant of the exact solution.This supercloseness will be used to constructa post-processing that increases the order of approximation to the gradient in the globalL~2-norm.