Computable exact bounds for linear outputs from stabilized solutions of the advection–diffusion–reaction equation. (18th September 2012)

• Record Type: Journal Article
• Authors: Parés, Núria; Díez, Pedro; Huerta, Antonio
• Is Part Of: International journal for numerical methods in engineering. Volume 93:Number 5(2013)
• Page Start: 483
• Page End: 509
• Publication Date: 2012-09-18
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4396
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4396-abs-0001"> <title>SUMMARY</title> <p>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 <italic>hybrid‐flux</italic> and <italic>flux‐free</italic> 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 <italic>flux‐free</italic> technique. Copyright © 2012 John Wiley &amp; Sons, Ltd.</p> </abstract>