Premium
Computable exact bounds for linear outputs from stabilized solutions of the advection–diffusion–reaction equation
Author(s) -
Parés Núria,
Díez Pedro,
Huerta Antonio
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4396
Subject(s) - estimator , a priori and a posteriori , mathematics , advection , galerkin method , finite element method , discontinuous galerkin method , exact solutions in general relativity , diffusion , reaction–diffusion system , flux (metallurgy) , mathematical analysis , physics , thermodynamics , chemistry , statistics , organic chemistry , philosophy , epistemology
SUMMARY 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.