Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities

Abstract

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.