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

TL;DR

This paper proves a supercloseness property of order p+1/4 for higher-order Galerkin finite element methods applied to singularly perturbed convection-diffusion problems, using solution decomposition and special finite element representations.

Contribution

It provides the first supercloseness analysis for higher-order Galerkin FEM in convection-diffusion problems, establishing a specific order of supercloseness.

Findings

Supercloseness of order p+1/4 in energy norm for p>=3 odd

Use of solution decomposition and special finite element space representation

First such analysis for higher-order Galerkin FEM in this context

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