Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Mark Ainsworth; Alejandro Allendes; Gabriel R. Barrenechea; Richard Rankin

doi:10.1002/fld.3822

Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin

Research output: Journal Publication › Article › peer-review

25 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	765-790
Number of pages	26
Journal	International Journal for Numerical Methods in Fluids
Volume	73
Issue number	9
DOIs	https://doi.org/10.1002/fld.3822
Publication status	Published - 30 Nov 2013
Externally published	Yes

Keywords

3D convection-reaction-diffusion
Fully computable a posteriori error estimator
SUPG stabilised method

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Computer Science Applications
Applied Mathematics

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10.1002/fld.3822

Cite this

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abstract = "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.",

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Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. / Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R. et al.
In: International Journal for Numerical Methods in Fluids, Vol. 73, No. 9, 30.11.2013, p. 765-790.

Research output: Journal Publication › Article › peer-review

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AU - Allendes, Alejandro

AU - Barrenechea, Gabriel R.

AU - Rankin, Richard

PY - 2013/11/30

Y1 - 2013/11/30

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AB - 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.

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KW - Fully computable a posteriori error estimator

KW - SUPG stabilised method

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Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions

Abstract

Keywords

ASJC Scopus subject areas

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