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

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 order p+1/4 in the energy norm where the polynomial order p>=3 is odd.