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

Authors:
F. Brezzi;T. J. R. Hughes;L. D. Marini;A. Russo;E. Süli
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1999

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Abstract

We develop an a priori error analysis of a finite element approximation to the elliptic advection-diffusion equation $-\eps \Delta u + \conv\cdot \nabla u = f$ 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 \[ \biggl(\eps \|\nabla v\|^2_{L_2(\Omega)} + \sum_{T} h_T\|\conv\cdot \nabla v\|^2_{L_2(T)}\biggr)^{1/2},\] where hT denotes the diameter of element T in the subdivision of the computational domain.