(untitled) (Journal of Computational Mathematics, 2018)
For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^2-projection from the piecewise constant field ∇u_N to the continuous and piecewise linear finite element space gives a better approximation of ∇u in the H^1-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.