Superconvergence Using Pointwise Interpolation in Convection-Diffusion Problems

TL;DR

This paper demonstrates superconvergence in convection-diffusion problems using pointwise interpolation in higher-order streamline diffusion FEM, revealing connections between interpolation types and analyzing postprocessing operators.

Contribution

It introduces a novel analysis of superconvergence via pointwise Gau{a4ss-Lobatto interpolation and links it to vertex-edge-cell interpolants in convection-diffusion FEM.

Findings

Superconvergence achieved with pointwise interpolation in FEM.

Connection established between different interpolation methods.

Postprocessing operators enhance solution accuracy.

Abstract

Considering a singularly perturbed convection-diffusion problem, we present an analysis for a superconvergence result using pointwise interpolation of Gau{\ss}-Lobatto type for higher-order streamline diffusion FEM. We show a useful connection between two different types of interpolation, namely a vertex-edge-cell interpolant and a pointwise interpolant. Moreover, different postprocessing operators are analysed and applied to model problems.