Solution of a Scalar Convection-Diffusion Equation using FEMLAB

TL;DR

This paper demonstrates how FEMLAB 3.1 can effectively solve steady scalar convection-diffusion equations in 1D and 2D, reducing oscillations and validating results against analytical solutions.

Contribution

It introduces the application of FEMLAB 3.1 for convection-diffusion problems, highlighting its ability to mitigate oscillations in convection-dominated cases.

Findings

FEMLAB 3.1 successfully reduces unrealistic oscillations.

Solutions closely match analytical results.

Applicability to 1D and 2D problems demonstrated.

Abstract

A steady scalar convection-diffusion problem has been studied for one and two dimensional cases. The major problem of unrealistic oscillations of the convection dominated problems is relaxed thanks to the wide range of the elements FEMLAB 3.1 benefits. The FEMLAB 3.1 solution has been presented for the problems, unique features and illustrations of the software have been used and results have been tested against analytic solution.