Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

Abstract

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space, we are able to prove a supercloseness property of $p + 1/4$ in the energy norm where the polynomial order $p ≥ 3$ is odd.