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

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...

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Published in:International journal for numerical methods in engineering 2013-02, Vol.93 (5), p.483-509
Main Authors: Parés, Núria, Díez, Pedro, Huerta, Antonio
Format: Article
Language:English
Subjects:
65 Numerical analysis
advection-diffusion-reaction equation
Anàlisi numèrica
Classificació AMS
Equacions diferencials parcials
error estimation
Errors
Estimates
Exact solutions
exact/guaranteed/strict bounds
Galerkin methods
goal-oriented adaptivity
linear-functional outputs
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Methodology
Numerical analysis
Reproduction
stabilization methods
Àrees temàtiques de la UPC
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container_title International journal for numerical methods in engineering
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creator Parés, Núria
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Huerta, Antonio
description 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.
doi_str_mv 10.1002/nme.4396
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source Wiley-Blackwell Read & Publish Collection
subjects 65 Numerical analysis
advection-diffusion-reaction equation
Anàlisi numèrica
Classificació AMS
Equacions diferencials parcials
error estimation
Errors
Estimates
Exact solutions
exact/guaranteed/strict bounds
Galerkin methods
goal-oriented adaptivity
linear-functional outputs
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Methodology
Numerical analysis
Reproduction
stabilization methods
Àrees temàtiques de la UPC
title Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation
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