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Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions
Author(s) -
Ainsworth Mark,
Allendes Alejandro,
Barrenechea Gabriel R.,
Rankin Richard
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3822
Subject(s) - discretization , estimator , mathematics , upper and lower bounds , finite element method , a priori and a posteriori , norm (philosophy) , convection–diffusion equation , approximations of π , polygon mesh , mathematical analysis , geometry , physics , thermodynamics , statistics , philosophy , epistemology , political science , law
SUMMARY 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 & Sons, Ltd.