Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities (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.