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

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.