A Priori Error Analysis of Residual-Free Bubbles for Advection-Diffusion Problems

Abstract

We develop an a priori error analysis of a finite element approximation to the elliptic advection-diffusion equation -ε△u + a · ▽u = f subject to a homogeneous Dirichlet boundary condition, based on the use of residual-free bubble functions. An optimal order error bound is derived in the so-called stability-norm (ε||▽v||2L2(Ω) + ∑ThT||a · ▽v||2L2(T))1/2, where hT denotes the diameter of element T in the subdivision of the computational domain.