Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions. (24th July 2013)

• Record Type: Journal Article
• Authors: Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
• Is Part Of: International journal for numerical methods in fluids. Volume 73:Number 9(2013:Nov.)
• Page Start: 765
• Page End: 790
• Publication Date: 2013-07-24
• Subjects: Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.3822
• Languages: English
• ISSNs: 0271-2091

Abstract

<abstract abstract-type="main" id="fld3822-abs-0001"> <title>SUMMARY</title> <p id="fld3822-para-0001">Fully computable upper bounds are developed for the discretisation error measured in the natural (energy) norm for convection–reaction–diffusion problems in three dimensions. The upper bounds are genuine upper bounds in the sense that the numerical value of the estimated error exceeds the actual numerical value of the true error regardless of the coarseness of the mesh or the nature of the data for the problem. All constants appearing in the bounds are fully specified. Examples show the estimator to be reliable and accurate even in the case of complicated three‐dimensional problems. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>