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

In this paper we present a first supercloseness analysis for higher-orderGalerkin FEM applied to a singularly perturbed convection-diffusion problem. Usinga 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 wherethe polynomial order $p ≥ 3$ is odd.