Stabilization with residual-free bubbles for advection-dominated transport equations

TL;DR

This paper introduces an enhanced finite element method using residual-free bubbles to improve stability and efficiency in solving advection-dominated transport equations, especially at high Peclet numbers.

Contribution

It presents a novel stabilized FEM scheme with residual-free bubbles that outperforms traditional hp-FEM in stability and computational efficiency for advection-dominated problems.

Findings

Improved stability in high-Peclet number regimes

Enhanced computational performance over traditional methods

Effective stabilization demonstrated on benchmark problems

Abstract

An improved numerical scheme is proposed for advection-dominated advection-diffusion problem. The scheme is based on Galerkin finite element method (FEM) with basis enriched with approximations to residual-free bubbles. The stabilisation effect of the numerical scheme was studied on several benchmark problems with high-Peclet numbers. Comparison to traditional hp-FEM, reveals improved stability and computational performance.