Computable exact bounds for linear outputs from stabilized solutions of the advection–diffusion–reaction equation


Núria Parés, Matemàtica Aplicada III, EUETIB, Comte d'Urgell 187, Barcelona, Spain.



The paper introduces a methodology to compute strict upper and lower bounds for linear-functional outputs of the exact solutions of the advection–diffusion–reaction equation. The bounds are computed using implicit a posteriori error estimators from stabilized finite element approximations of the exact solution. The new methodology extends the a posteriori error estimates yielding bounds for the standard Galerkin formulation to be able to obtain bounds for stabilized formulations. This methodology is combined with both hybrid-flux and flux-free techniques for error assessment. The application to stabilized formulations provides sharper estimates than when applied to Galerkin methods. The best results are found in combination with the flux-free technique. Copyright © 2012 John Wiley & Sons, Ltd.